Aliyeva, S. T. First- and second-order necessary optimality conditions for a control problem described by nonlinear fractional difference equations. (English. Russian original) Zbl 1521.93086 Autom. Remote Control 84, No. 3, 187-195 (2023); translation from Avtom. Telemekh. 2023, No. 2, 54-65 (2023). MSC: 93C23 39A99 26A33 49K21 PDFBibTeX XMLCite \textit{S. T. Aliyeva}, Autom. Remote Control 84, No. 3, 187--195 (2023; Zbl 1521.93086); translation from Avtom. Telemekh. 2023, No. 2, 54--65 (2023) Full Text: DOI
Liu, Chongyang; Shi, Guoqing; Liu, Gang; Hu, Dianzhong Optimal control of a nonlinear state-dependent impulsive system in fed-batch process. (English) Zbl 1519.92130 Int. J. Biomath. 16, No. 8, Article ID 2350001, 28 p. (2023). MSC: 92C75 49N25 93C10 PDFBibTeX XMLCite \textit{C. Liu} et al., Int. J. Biomath. 16, No. 8, Article ID 2350001, 28 p. (2023; Zbl 1519.92130) Full Text: DOI
Ferreira, Rui A. C. Sign of the solutions of linear fractional differential equations and some applications. (English) Zbl 07683071 Vietnam J. Math. 51, No. 2, 451-461 (2023). Reviewer: Syed Abbas (Mandi) MSC: 34A08 34A30 34A12 26A33 49K30 PDFBibTeX XMLCite \textit{R. A. C. Ferreira}, Vietnam J. Math. 51, No. 2, 451--461 (2023; Zbl 07683071) Full Text: DOI arXiv
Durastanti, Riccardo; Giacomelli, Lorenzo Spreading equilibria under mildly singular potentials: pancakes versus droplets. (English) Zbl 1503.35158 J. Nonlinear Sci. 32, No. 5, Paper No. 71, 61 p. (2022). MSC: 35Q35 34C60 34E10 35J91 49J05 49J10 76A20 76D03 76D08 35R35 35A02 PDFBibTeX XMLCite \textit{R. Durastanti} and \textit{L. Giacomelli}, J. Nonlinear Sci. 32, No. 5, Paper No. 71, 61 p. (2022; Zbl 1503.35158) Full Text: DOI arXiv
Cresson, Jacky; Jiménez, Fernando; Ober-Blöbaum, Sina Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. (English) Zbl 1487.49027 J. Geom. Mech. 14, No. 1, 57-89 (2022). MSC: 49K21 26A33 70G65 37M15 PDFBibTeX XMLCite \textit{J. Cresson} et al., J. Geom. Mech. 14, No. 1, 57--89 (2022; Zbl 1487.49027) Full Text: DOI
Fagbemigun, Bosede. O.; Mogbademu, Adesanmi. A. Hermite-Hadamard inequality for coordinated \(F_h\)-convex functions on time scales. (English) Zbl 1486.26031 Palest. J. Math. 10, No. 2, 633-643 (2021). MSC: 26D10 34N05 39A10 49K35 PDFBibTeX XMLCite \textit{Bosede. O. Fagbemigun} and \textit{Adesanmi. A. Mogbademu}, Palest. J. Math. 10, No. 2, 633--643 (2021; Zbl 1486.26031) Full Text: Link
Ren, Qiu-Yan; Sun, Jian-Ping Optimality necessary conditions for an optimal control problem on time scales. (English) Zbl 1484.49050 AIMS Math. 6, No. 6, 5639-5646 (2021). MSC: 49K21 26E70 34N05 PDFBibTeX XMLCite \textit{Q.-Y. Ren} and \textit{J.-P. Sun}, AIMS Math. 6, No. 6, 5639--5646 (2021; Zbl 1484.49050) Full Text: DOI
Stanzhytskyi, O.; Mogylova, V.; Lavrova, O. Optimal control for systems of differential equations on the infinite interval of time scale. (English) Zbl 1483.49012 Sadovnichiy, Victor A. (ed.) et al., Contemporary approaches and methods in fundamental mathematics and mechanics. Cham: Springer. Underst. Complex Syst., 395-405 (2021). Reviewer: Souvik Roy (Arlington) MSC: 49J15 PDFBibTeX XMLCite \textit{O. Stanzhytskyi} et al., in: Contemporary approaches and methods in fundamental mathematics and mechanics. Cham: Springer. 395--405 (2021; Zbl 1483.49012) Full Text: DOI
Shen, Yonghong Mean value theorem and semigroups of operators for interval-valued functions on time scales. (English) Zbl 1488.49038 Hacet. J. Math. Stat. 50, No. 1, 79-91 (2021). MSC: 49J53 54C60 58C06 PDFBibTeX XMLCite \textit{Y. Shen}, Hacet. J. Math. Stat. 50, No. 1, 79--91 (2021; Zbl 1488.49038) Full Text: DOI
Bettiol, Piernicola; Bourdin, Loïc Pontryagin maximum principle for state constrained optimal sampled-data control problems on time scales. (English) Zbl 1470.49045 ESAIM, Control Optim. Calc. Var. 27, Paper No. 51, 36 p. (2021). Reviewer: Hector O. Fattorini (Los Angeles) MSC: 49K15 49J35 26E70 34H05 34K35 34N05 39A12 PDFBibTeX XMLCite \textit{P. Bettiol} and \textit{L. Bourdin}, ESAIM, Control Optim. Calc. Var. 27, Paper No. 51, 36 p. (2021; Zbl 1470.49045) Full Text: DOI
Zhu, Yingjun; Jia, Guangyan Stochastic linear quadratic control problem on time scales. (English) Zbl 1465.93231 Discrete Dyn. Nat. Soc. 2021, Article ID 5743014, 12 p. (2021). MSC: 93E20 34N05 49N10 93B52 PDFBibTeX XMLCite \textit{Y. Zhu} and \textit{G. Jia}, Discrete Dyn. Nat. Soc. 2021, Article ID 5743014, 12 p. (2021; Zbl 1465.93231) Full Text: DOI
Anerot, Baptiste; Cresson, Jacky; Hariz Belgacem, Khaled; Pierret, Frederic Noether’s-type theorems on time scales. (English) Zbl 1466.49019 J. Math. Phys. 61, No. 11, 113502, 31 p. (2020). MSC: 49K05 26E70 34N05 70S10 PDFBibTeX XMLCite \textit{B. Anerot} et al., J. Math. Phys. 61, No. 11, 113502, 31 p. (2020; Zbl 1466.49019) Full Text: DOI HAL
Zhu, Yingjun; Jia, Guangyan Linear feedback of mean-field stochastic linear quadratic optimal control problems on time scales. (English) Zbl 1459.49024 Math. Probl. Eng. 2020, Article ID 8051918, 11 p. (2020). MSC: 49N80 26E70 34N05 49N10 60H10 93E20 PDFBibTeX XMLCite \textit{Y. Zhu} and \textit{G. Jia}, Math. Probl. Eng. 2020, Article ID 8051918, 11 p. (2020; Zbl 1459.49024) Full Text: DOI
Song, Chuan-Jing; Cheng, Yao Noether’s theorems for nonshifted dynamic systems on time scales. (English) Zbl 1433.70030 Appl. Math. Comput. 374, Article ID 125086, 12 p. (2020). MSC: 70H05 26E70 34N05 49K05 PDFBibTeX XMLCite \textit{C.-J. Song} and \textit{Y. Cheng}, Appl. Math. Comput. 374, Article ID 125086, 12 p. (2020; Zbl 1433.70030) Full Text: DOI
E, Weinan; Han, Jiequn; Li, Qianxiao A mean-field optimal control formulation of deep learning. (English) Zbl 1421.49021 Res. Math. Sci. 6, No. 1, Paper No. 10, 41 p. (2019). MSC: 49K21 92B20 PDFBibTeX XMLCite \textit{W. E} et al., Res. Math. Sci. 6, No. 1, Paper No. 10, 41 p. (2019; Zbl 1421.49021) Full Text: DOI arXiv
Jin, Shi-Xin; Zhang, Yi Reduction of Chaplygin equations for nonholonomic systems on time scales by means of the cyclic integral and energy integral. (English) Zbl 07822187 Chin. J. Phys., Taipei 56, No. 6, 2731-2740 (2018). MSC: 49Kxx 39Axx 70Hxx PDFBibTeX XMLCite \textit{S.-X. Jin} and \textit{Y. Zhang}, Chin. J. Phys., Taipei 56, No. 6, 2731--2740 (2018; Zbl 07822187) Full Text: DOI
Šimon Hilscher, Roman; Zeidan, Vera Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. (English) Zbl 1415.49015 ESAIM, Control Optim. Calc. Var. 24, No. 4, 1705-1734 (2018). Reviewer: Gerhard-Wilhelm Weber (Poznań and Ankara) with Emel Savku (Palaiseau) MSC: 49K15 49K40 34N05 34K35 90C31 39A12 PDFBibTeX XMLCite \textit{R. Šimon Hilscher} and \textit{V. Zeidan}, ESAIM, Control Optim. Calc. Var. 24, No. 4, 1705--1734 (2018; Zbl 1415.49015) Full Text: DOI
Zhai, Xiang-Hua; Zhang, Yi Noether theorem for non-conservative systems with time delay on time scales. (English) Zbl 1510.49019 Commun. Nonlinear Sci. Numer. Simul. 52, 32-43 (2017). MSC: 49K21 39A10 PDFBibTeX XMLCite \textit{X.-H. Zhai} and \textit{Y. Zhang}, Commun. Nonlinear Sci. Numer. Simul. 52, 32--43 (2017; Zbl 1510.49019) Full Text: DOI
Song, Chuanjing; Zhang, Yi Noether theory for Birkhoffian systems with nabla derivatives. (English) Zbl 1412.34245 J. Nonlinear Sci. Appl. 10, No. 4, 2268-2282 (2017). MSC: 34N05 39A12 49K05 PDFBibTeX XMLCite \textit{C. Song} and \textit{Y. Zhang}, J. Nonlinear Sci. Appl. 10, No. 4, 2268--2282 (2017; Zbl 1412.34245) Full Text: DOI
Kichmarenko, O. D.; Ogulenko, A. P. Averaging of multicriteria control problems of systems on time scales. (English. Russian original) Zbl 1384.93079 J. Comput. Syst. Sci. Int. 56, No. 1, 33-43 (2017); translation from Kibern. Sist. Anal. 2017, No. 1, 36-45 (2017). MSC: 93C70 90C29 93B40 49M30 PDFBibTeX XMLCite \textit{O. D. Kichmarenko} and \textit{A. P. Ogulenko}, J. Comput. Syst. Sci. Int. 56, No. 1, 33--43 (2017; Zbl 1384.93079); translation from Kibern. Sist. Anal. 2017, No. 1, 36--45 (2017) Full Text: DOI
Lavrova, O. E. Conditions for the existence of optimal control for some classes of differential equations on time scales. (English. Ukrainian original) Zbl 1386.49005 J. Math. Sci., New York 222, No. 3, 276-295 (2017); translation from Neliniĭni Kolyvannya 19, No. 1, 67-84 (2016). Reviewer: Tullio Zolezzi (Genova) MSC: 49J21 PDFBibTeX XMLCite \textit{O. E. Lavrova}, J. Math. Sci., New York 222, No. 3, 276--295 (2017; Zbl 1386.49005); translation from Neliniĭni Kolyvannya 19, No. 1, 67--84 (2016) Full Text: DOI
Bohner, Martin; Streipert, Sabrina Optimal harvesting policy for the Beverton-Holt model. (English) Zbl 1348.39008 Math. Biosci. Eng. 13, No. 4, 673-695 (2016). MSC: 39A23 92D25 39A30 49K15 PDFBibTeX XMLCite \textit{M. Bohner} and \textit{S. Streipert}, Math. Biosci. Eng. 13, No. 4, 673--695 (2016; Zbl 1348.39008) Full Text: DOI
Ogulenko, A. P.; Kichmarenko, O. D. Averaging of the problem of optimal control on time scales. (English. Ukrainian original) Zbl 1334.49097 J. Math. Sci., New York 212, No. 3, 290-304 (2016); translation from Neliniĭni Kolyvannya 17, No. 3, 365-378 (2014). MSC: 49M30 49J21 34N05 PDFBibTeX XMLCite \textit{A. P. Ogulenko} and \textit{O. D. Kichmarenko}, J. Math. Sci., New York 212, No. 3, 290--304 (2016; Zbl 1334.49097); translation from Neliniĭni Kolyvannya 17, No. 3, 365--378 (2014) Full Text: DOI
Bourdin, Loïc; Trélat, Emmanuel Optimal sampled-data control, and generalizations on time scales. (English) Zbl 1335.49031 Math. Control Relat. Fields 6, No. 1, 53-94 (2016). MSC: 49K15 49J15 49K21 49J21 93C57 34N05 39A12 PDFBibTeX XMLCite \textit{L. Bourdin} and \textit{E. Trélat}, Math. Control Relat. Fields 6, No. 1, 53--94 (2016; Zbl 1335.49031) Full Text: DOI arXiv
Guzowska, Małgorzata; Malinowska, Agnieszka B.; Sidi Ammi, Moulay Rchid Calculus of variations on time scales: applications to economic models. (English) Zbl 1422.49021 Adv. Difference Equ. 2015, Paper No. 203, 15 p. (2015). MSC: 49K05 39A12 34N05 PDFBibTeX XMLCite \textit{M. Guzowska} et al., Adv. Difference Equ. 2015, Paper No. 203, 15 p. (2015; Zbl 1422.49021) Full Text: DOI
Janglajew, Klara; Pawłuszewicz, Ewa Constrained local controllability of dynamic systems on time scales. (English) Zbl 1343.34212 Adv. Difference Equ. 2015, Paper No. 89, 8 p. (2015). MSC: 34N05 49K21 93C05 34H05 PDFBibTeX XMLCite \textit{K. Janglajew} and \textit{E. Pawłuszewicz}, Adv. Difference Equ. 2015, Paper No. 89, 8 p. (2015; Zbl 1343.34212) Full Text: DOI
Carlson, Dean A. The existence of optimal controls for problems defined on time scales. (English) Zbl 1328.49004 J. Optim. Theory Appl. 166, No. 2, 351-376 (2015). Reviewer: Fredi Tröltzsch (Berlin) MSC: 49J21 49J15 34N05 26E70 PDFBibTeX XMLCite \textit{D. A. Carlson}, J. Optim. Theory Appl. 166, No. 2, 351--376 (2015; Zbl 1328.49004) Full Text: DOI
Santos, Iguer L. D.; Silva, Geraldo N. Filippov’s selection theorem and the existence of solutions for optimal control problems in time scales. (English) Zbl 1306.49008 Comput. Appl. Math. 33, No. 1, 223-241 (2014). MSC: 49J21 49J53 49J15 37N35 PDFBibTeX XMLCite \textit{I. L. D. Santos} and \textit{G. N. Silva}, Comput. Appl. Math. 33, No. 1, 223--241 (2014; Zbl 1306.49008) Full Text: DOI
Malinowska, Agnieszka B.; Martins, Natália The second Noether theorem on time scales. (English) Zbl 1470.49042 Abstr. Appl. Anal. 2013, Article ID 675127, 14 p. (2013). MSC: 49K10 26E70 PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{N. Martins}, Abstr. Appl. Anal. 2013, Article ID 675127, 14 p. (2013; Zbl 1470.49042) Full Text: DOI arXiv
Ryckelynck, P.; Smoch, L. Discrete calculus of variations for quadratic Lagrangians. (English) Zbl 1275.49040 Commun. Math. Anal. 15, No. 1, 44-60 (2013). MSC: 49K21 49K15 49N10 49M25 PDFBibTeX XMLCite \textit{P. Ryckelynck} and \textit{L. Smoch}, Commun. Math. Anal. 15, No. 1, 44--60 (2013; Zbl 1275.49040) Full Text: Euclid
El-Nabulsi, Rami Ahmad Calculus of variations with hyperdifferential operators from Tabasaki-Takebe-Toda lattice arguments. (English) Zbl 1275.49034 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 107, No. 2, 419-436 (2013). MSC: 49K15 37N35 PDFBibTeX XMLCite \textit{R. A. El-Nabulsi}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 107, No. 2, 419--436 (2013; Zbl 1275.49034) Full Text: DOI
Cresson, Jacky; Malinowska, Agnieszka B.; Torres, Delfim F. M. Time scale differential, integral, and variational embeddings of Lagrangian systems. (English) Zbl 1268.49030 Comput. Math. Appl. 64, No. 7, 2294-2301 (2012). MSC: 49K21 34N05 26E70 PDFBibTeX XMLCite \textit{J. Cresson} et al., Comput. Math. Appl. 64, No. 7, 2294--2301 (2012; Zbl 1268.49030) Full Text: DOI arXiv
Brito da Cruz, Artur M. C.; Martins, Natália The \(q\)-symmetric variational calculus. (English) Zbl 1268.49029 Comput. Math. Appl. 64, No. 7, 2241-2250 (2012). MSC: 49K21 39A13 PDFBibTeX XMLCite \textit{A. M. C. Brito da Cruz} and \textit{N. Martins}, Comput. Math. Appl. 64, No. 7, 2241--2250 (2012; Zbl 1268.49029) Full Text: DOI
Martins, Natália; Torres, Delfim F. M. Necessary optimality conditions for higher-order infinite horizon variational problems on time scales. (English) Zbl 1280.49009 J. Optim. Theory Appl. 155, No. 2, 453-476 (2012). Reviewer: Fredi Tröltzsch (Berlin) MSC: 49J21 49K21 PDFBibTeX XMLCite \textit{N. Martins} and \textit{D. F. M. Torres}, J. Optim. Theory Appl. 155, No. 2, 453--476 (2012; Zbl 1280.49009) Full Text: DOI arXiv
Girejko, Ewa; Malinowska, Agnieszka B.; Torres, Delfim F. M. The contingent epiderivative and the calculus of variations on time scales. (English) Zbl 1239.49025 Optimization 61, No. 1-3, 251-264 (2012). MSC: 49K05 26E70 34N05 PDFBibTeX XMLCite \textit{E. Girejko} et al., Optimization 61, No. 1--3, 251--264 (2012; Zbl 1239.49025) Full Text: DOI arXiv
Šimon Hilscher, Roman; Zeidan, Vera Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. (English) Zbl 1230.49023 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 2, 932-950 (2012). MSC: 49L20 49K15 93C10 49N10 34N05 PDFBibTeX XMLCite \textit{R. Šimon Hilscher} and \textit{V. Zeidan}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 2, 932--950 (2012; Zbl 1230.49023) Full Text: DOI
Girejko, Ewa; Malinowska, Agnieszka B.; Torres, Delfim F. M. Delta-nabla optimal control problems. (English) Zbl 1271.49013 J. Vib. Control 17, No. 11, 1634-1643 (2011). MSC: 49K05 PDFBibTeX XMLCite \textit{E. Girejko} et al., J. Vib. Control 17, No. 11, 1634--1643 (2011; Zbl 1271.49013) Full Text: DOI arXiv
Bartosiewicz, Zbigniew; Martins, Natália; Torres, Delfim F. M. The second Euler-Lagrange equation of variational calculus on time scales. (English) Zbl 1248.49024 Eur. J. Control 17, No. 1, 9-18 (2011). MSC: 49K15 34H05 PDFBibTeX XMLCite \textit{Z. Bartosiewicz} et al., Eur. J. Control 17, No. 1, 9--18 (2011; Zbl 1248.49024) Full Text: DOI arXiv
Šimon Hilscher, Roman; Zeidan, Vera First order conditions for generalized variational problems over time scales. (English) Zbl 1236.49061 Comput. Math. Appl. 62, No. 9, 3490-3503 (2011). MSC: 49K21 34N05 PDFBibTeX XMLCite \textit{R. Šimon Hilscher} and \textit{V. Zeidan}, Comput. Math. Appl. 62, No. 9, 3490--3503 (2011; Zbl 1236.49061) Full Text: DOI
Cui, Yujun; Sun, Jingxian Fixed point theorems for a class of nonlinear operators in Hilbert spaces and applications. (English) Zbl 1234.49009 Positivity 15, No. 3, 455-464 (2011). MSC: 49J35 47H10 58E30 PDFBibTeX XMLCite \textit{Y. Cui} and \textit{J. Sun}, Positivity 15, No. 3, 455--464 (2011; Zbl 1234.49009) Full Text: DOI
Malinowska, Agnieszka B.; Torres, Delfim F. M. A general backwards calculus of variations via duality. (English) Zbl 1229.49034 Optim. Lett. 5, No. 4, 587-599 (2011). MSC: 49N15 49K15 PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{D. F. M. Torres}, Optim. Lett. 5, No. 4, 587--599 (2011; Zbl 1229.49034) Full Text: DOI arXiv
Martins, Natália; Torres, Delfim F. M. Generalizing the variational theory on time scales to include the delta indefinite integral. (English) Zbl 1221.49040 Comput. Math. Appl. 61, No. 9, 2424-2435 (2011). MSC: 49K21 34A08 PDFBibTeX XMLCite \textit{N. Martins} and \textit{D. F. M. Torres}, Comput. Math. Appl. 61, No. 9, 2424--2435 (2011; Zbl 1221.49040) Full Text: DOI arXiv
Liu, G.; Xiang, X.; Peng, Y. Nonlinear integro-differential equations and optimal control problems on time scales. (English) Zbl 1211.34116 Comput. Math. Appl. 61, No. 2, 155-169 (2011). MSC: 34N05 45J05 49K21 PDFBibTeX XMLCite \textit{G. Liu} et al., Comput. Math. Appl. 61, No. 2, 155--169 (2011; Zbl 1211.34116) Full Text: DOI
Bastos, Nuno R. O.; Ferreira, Rui A. C.; Torres, Delfim F. M. Discrete-time fractional variational problems. (English) Zbl 1203.94022 Signal Process. 91, No. 3, 513-524 (2011). MSC: 94A12 26A33 62M10 49J99 PDFBibTeX XMLCite \textit{N. R. O. Bastos} et al., Signal Process. 91, No. 3, 513--524 (2011; Zbl 1203.94022) Full Text: DOI arXiv
Ferreira, Rui A. C.; Malinowska, Agnieszka B.; Torres, Delfim F. M. Optimality conditions for the calculus of variations with higher-order delta derivatives. (English) Zbl 1208.49020 Appl. Math. Lett. 24, No. 1, 87-92 (2011). MSC: 49K15 34N05 93C70 PDFBibTeX XMLCite \textit{R. A. C. Ferreira} et al., Appl. Math. Lett. 24, No. 1, 87--92 (2011; Zbl 1208.49020) Full Text: DOI arXiv
Malinowska, A. B.; Torres, D. F. M. The Hahn quantum variational calculus. (English) Zbl 1218.49026 J. Optim. Theory Appl. 147, No. 3, 419-442 (2010). MSC: 49K10 81Q93 PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{D. F. M. Torres}, J. Optim. Theory Appl. 147, No. 3, 419--442 (2010; Zbl 1218.49026) Full Text: DOI arXiv
Malinowska, Agnieszka B.; Torres, Delfim F. M. Leitmann’s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales. (English) Zbl 1200.49022 Appl. Math. Comput. 217, No. 3, 1158-1162 (2010). MSC: 49K15 PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{D. F. M. Torres}, Appl. Math. Comput. 217, No. 3, 1158--1162 (2010; Zbl 1200.49022) Full Text: DOI arXiv
Martins, Natália; Torres, Delfim F. M. Noether’s symmetry theorem for nabla problems of the calculus of variations. (English) Zbl 1205.49033 Appl. Math. Lett. 23, No. 12, 1432-1438 (2010). MSC: 49K21 49N15 PDFBibTeX XMLCite \textit{N. Martins} and \textit{D. F. M. Torres}, Appl. Math. Lett. 23, No. 12, 1432--1438 (2010; Zbl 1205.49033) Full Text: DOI arXiv
Malinowska, Agnieszka B.; Torres, Delfim F. M. Natural boundary conditions in the calculus of variations. (English) Zbl 1196.49014 Math. Methods Appl. Sci. 33, No. 14, 1712-1722 (2010). MSC: 49K05 39A12 93C70 93C55 PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{D. F. M. Torres}, Math. Methods Appl. Sci. 33, No. 14, 1712--1722 (2010; Zbl 1196.49014) Full Text: DOI arXiv
Almeida, Ricardo; Torres, Delfim F. M. Isoperimetric problems on time scales with nabla derivatives. (English) Zbl 1273.49024 J. Vib. Control 15, No. 6, 951-958 (2009). MSC: 49K05 91B99 PDFBibTeX XMLCite \textit{R. Almeida} and \textit{D. F. M. Torres}, J. Vib. Control 15, No. 6, 951--958 (2009; Zbl 1273.49024) Full Text: DOI arXiv
Martins, Natália; Torres, Delfim F. M. Calculus of variations on time scales with nabla derivatives. (English) Zbl 1238.49037 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e763-e773 (2009). MSC: 49K21 34N05 PDFBibTeX XMLCite \textit{N. Martins} and \textit{D. F. M. Torres}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e763--e773 (2009; Zbl 1238.49037) Full Text: DOI arXiv
Abdeljawad, Thabet; Jarad, Fahd; Baleanu, Dumitru Variational optimal-control problems with delayed arguments on time scales. (English) Zbl 1184.49023 Adv. Difference Equ. 2009, Article ID 840386, 15 p. (2009). MSC: 49K15 34N05 34H05 PDFBibTeX XMLCite \textit{T. Abdeljawad} et al., Adv. Difference Equ. 2009, Article ID 840386, 15 p. (2009; Zbl 1184.49023) Full Text: DOI arXiv EuDML
Malinowska, A. B.; Torres, D. F. M. Necessary and sufficient conditions for local Pareto optimality on time scales. (English. Russian original) Zbl 1192.49022 J. Math. Sci., New York 161, No. 6, 803-810 (2009); translation from Sovrem. Mat. Prilozh. 63 (2009). MSC: 49K10 90C29 93C30 PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{D. F. M. Torres}, J. Math. Sci., New York 161, No. 6, 803--810 (2009; Zbl 1192.49022); translation from Sovrem. Mat. Prilozh. 63 (2009) Full Text: DOI arXiv
Zhan, Zaidong; Wei, W. On existence of optimal control governed by a class of the first-order linear dynamic systems on time scales. (English) Zbl 1183.49005 Appl. Math. Comput. 215, No. 6, 2070-2081 (2009). MSC: 49J15 93C70 PDFBibTeX XMLCite \textit{Z. Zhan} and \textit{W. Wei}, Appl. Math. Comput. 215, No. 6, 2070--2081 (2009; Zbl 1183.49005) Full Text: DOI
Hong, Shihuang Differentiability of multivalued functions on time scales and applications to multivalued dynamic equations. (English) Zbl 1172.26327 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, 3622-3637 (2009). Reviewer: Sergei V. Rogosin (Minsk) MSC: 26E25 49J53 PDFBibTeX XMLCite \textit{S. Hong}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, 3622--3637 (2009; Zbl 1172.26327) Full Text: DOI
Zhan, Zaidong; Wei, W. Necessary conditions for a class of optimal control problems on time scales. (English) Zbl 1163.49013 Abstr. Appl. Anal. 2009, Article ID 974394, 14 p. (2009). MSC: 49J50 49K15 PDFBibTeX XMLCite \textit{Z. Zhan} and \textit{W. Wei}, Abstr. Appl. Anal. 2009, Article ID 974394, 14 p. (2009; Zbl 1163.49013) Full Text: DOI EuDML
Hilscher, Roman; Zeidan, Vera Weak maximum principle and accessory problem for control problems on time scales. (English) Zbl 1157.49030 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3209-3226 (2009). MSC: 49K15 39A12 34K35 49N25 93B05 93C15 93C55 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3209--3226 (2009; Zbl 1157.49030) Full Text: DOI
Bartosiewicz, Zbigniew; Torres, Delfim F. M. Noether’s theorem on time scales. (English) Zbl 1357.49081 J. Math. Anal. Appl. 342, No. 2, 1220-1226 (2008). MSC: 49K05 34N05 PDFBibTeX XMLCite \textit{Z. Bartosiewicz} and \textit{D. F. M. Torres}, J. Math. Anal. Appl. 342, No. 2, 1220--1226 (2008; Zbl 1357.49081) Full Text: DOI arXiv
Hilscher, Roman; Zeidan, Vera Riccati equations for abnormal time scale quadratic functionals. (English) Zbl 1355.49031 J. Differ. Equations 244, No. 6, 1410-1447 (2008). MSC: 49N10 34N05 39A10 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Differ. Equations 244, No. 6, 1410--1447 (2008; Zbl 1355.49031) Full Text: DOI
Bohner, Martin; Guseinov, Gusein Sh. Double integral calculus of variations on time scales. (English) Zbl 1131.49019 Comput. Math. Appl. 54, No. 1, 45-57 (2007). MSC: 49K10 39A10 26B99 PDFBibTeX XMLCite \textit{M. Bohner} and \textit{G. Sh. Guseinov}, Comput. Math. Appl. 54, No. 1, 45--57 (2007; Zbl 1131.49019) Full Text: DOI
Ma, Manjun; Guo, Zhiming Homoclinic orbits and subharmonics for nonlinear second order difference equations. (English) Zbl 1120.39007 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 6, 1737-1745 (2007). Reviewer: Christian Pötzsche (München) MSC: 39A14 37C29 49J40 PDFBibTeX XMLCite \textit{M. Ma} and \textit{Z. Guo}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 6, 1737--1745 (2007; Zbl 1120.39007) Full Text: DOI
Atici, Ferhan M.; Biles, Daniel C.; Lebedinsky, Alex An application of time scales to economics. (English) Zbl 1187.91125 Math. Comput. Modelling 43, No. 7-8, 718-726 (2006). MSC: 91B62 39A10 49K30 PDFBibTeX XMLCite \textit{F. M. Atici} et al., Math. Comput. Modelling 43, No. 7--8, 718--726 (2006; Zbl 1187.91125) Full Text: DOI
Yu, Jianshe; Guo, Zhiming Boundary value problems of discrete generalized Emden-Fowler equation. (English) Zbl 1117.39014 Sci. China, Ser. A 49, No. 10, 1303-1314 (2006). Reviewer: Sui Sun Cheng (Hsinchu) MSC: 39A12 39A11 49J40 PDFBibTeX XMLCite \textit{J. Yu} and \textit{Z. Guo}, Sci. China, Ser. A 49, No. 10, 1303--1314 (2006; Zbl 1117.39014) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey. (English) Zbl 1098.49025 J. Difference Equ. Appl. 11, No. 9, 857-875 (2005). MSC: 49K30 39A12 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Difference Equ. Appl. 11, No. 9, 857--875 (2005; Zbl 1098.49025) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Calculus of variations on time scales: Weak local piecewise \(C_{\text{rd}}^{1}\) solutions with variable endpoints. (English) Zbl 1043.49004 J. Math. Anal. Appl. 289, No. 1, 143-166 (2004). Reviewer: Ştefan Mirică (Bucureşti) MSC: 49J10 49K10 39A12 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Math. Anal. Appl. 289, No. 1, 143--166 (2004; Zbl 1043.49004) Full Text: DOI
Hilscher, R.; Zeidan, V. Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. (English) Zbl 1044.49020 Comput. Math. Appl. 45, No. 6-9, 1369-1383 (2003). MSC: 49K30 39A12 90C46 93C55 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, Comput. Math. Appl. 45, No. 6--9, 1369--1383 (2003; Zbl 1044.49020) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. (English) Zbl 1021.39008 Linear Algebra Appl. 367, 67-104 (2003). Reviewer: Yang En-Hao (Guangzhou) MSC: 39A12 93C55 49J15 65K10 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, Linear Algebra Appl. 367, 67--104 (2003; Zbl 1021.39008) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Coupled intervals in the discrete calculus of variations: necessity and sufficiency. (English) Zbl 1032.49038 J. Math. Anal. Appl. 276, No. 1, 396-421 (2002). Reviewer: Ştefan Mirică (Bucureşti) MSC: 49K30 49N10 39A12 39A13 93C55 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Math. Anal. Appl. 276, No. 1, 396--421 (2002; Zbl 1032.49038) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Second order sufficiency criteria for a discrete optimal control problem. (English) Zbl 1010.49020 J. Difference Equ. Appl. 8, No. 6, 573-602 (2002). Reviewer: Ştefan Mirică (Bucureşti) MSC: 49K99 39A10 39A12 93C55 93C10 49N10 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Difference Equ. Appl. 8, No. 6, 573--602 (2002; Zbl 1010.49020) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Discrete optimal control: Second order optimality conditions. (English) Zbl 1010.49021 J. Difference Equ. Appl. 8, No. 10, 875-896 (2002). Reviewer: Ondřej Došlý (Brno) MSC: 49K99 39A12 39A10 93C55 49N10 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Difference Equ. Appl. 8, No. 10, 875--896 (2002; Zbl 1010.49021) Full Text: DOI
Hilscher, Roman Positivity of quadratic functionals on time scales: Necessity. (English) Zbl 0999.34037 Math. Nachr. 226, 85-98 (2001). Reviewer: Wladyslaw Hejmo (Kraków) MSC: 34C10 93C70 49K15 39A10 PDFBibTeX XMLCite \textit{R. Hilscher}, Math. Nachr. 226, 85--98 (2001; Zbl 0999.34037) Full Text: DOI
Hilscher, Roman; Zeidan, Vera Discrete optimal control: The accessory problem and necessary optimality conditions. (English) Zbl 0987.49016 J. Math. Anal. Appl. 243, No. 2, 429-452 (2000). MSC: 49K30 PDFBibTeX XMLCite \textit{R. Hilscher} and \textit{V. Zeidan}, J. Math. Anal. Appl. 243, No. 2, 429--452 (2000; Zbl 0987.49016) Full Text: DOI
Agarwal, Ravi P.; Bohner, Martin Quadratic functionals for second order matrix equations on time scales. (English) Zbl 0938.49001 Nonlinear Anal., Theory Methods Appl. 33, No. 7, 675-692 (1998). Reviewer: W.Hejmo (Kraków) MSC: 49J15 49K15 34C10 39A10 PDFBibTeX XMLCite \textit{R. P. Agarwal} and \textit{M. Bohner}, Nonlinear Anal., Theory Methods Appl. 33, No. 7, 675--692 (1998; Zbl 0938.49001) Full Text: DOI