×
Mansouri, Bouzid; Ardjouni, Abdelouaheb; Djoudi, Ahcene

Positive solutions of nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. (English) Zbl 1490.34075

Nonauton. Dyn. Syst. 8, 297-306 (2021).
Summary: This paper provides sufficient conditions to guarantee the existence, uniqueness and continuous dependence of positive solutions of a nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. The main arguments are based on the Schauder fixed point theorem to prove the existence of a positive solution. As an application, we given an example to illustrate the obtained results.

MSC:

34K10 Boundary value problems for functional-differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

positive solutions; fourth order differential equations; iterative differential equations; boundary value problems; Schauder fixed point theorem
PDF BibTeX XML Cite
\textit{B. Mansouri} et al., Nonauton. Dyn. Syst. 8, 297--306 (2021; Zbl 1490.34075)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Benaicha, S., Haddouchi, F., Positive solutions of a nonlinear fourth-order integral boundary value problem, Analele Universităţii de Vest, Timişoara Seria Matematică-Informatică, LIV(1) (2016), 73-86. · Zbl 07644125
[2] Bouakkaz, A., Ardjouni, A., Djoudi, A., Periodic solutions for a nonlinear iterative functional differential equation, Electron. J. Math. Anal. Appl., 7(1) (2019), 156-166. · Zbl 1455.34070
[3] Bouakkaz, A., Ardjouni, A., Djoudi, A., Periodic solutions for a second order nonlinear functional differential equation with iterative terms by Schauder fixed point theorem, Acta Math. Univ. Comen., LXXXVII(2) (2018), 223-235. · Zbl 1424.34232
[4] Bouakkaz, A., Ardjouni, A., Khemis, R., Djoudi, A., Periodic solutions of a class of third-order functional differential equations with iterative source terms, Boletín de la Sociedad Matemática Mexicana, 26 (2020), 443-458. · Zbl 1458.34121
[5] Bouteraa, N., Benaicha, S., Djourdem, H., Positive Solutions for Systems of Fourth Order Two-Point Boundary Value Problems with Parameter, Journal of Mathematical Sciences and Modelling, 2(1) (2019), 30-38. · Zbl 1424.34092
[6] Cabadaa, A., Lopez-Somoza, L., Minhos, F., Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem, J. Nonlinear Sci. Appl., 10 (2017), 5445-5463. · Zbl 1412.34078
[7] Cheraiet, S., Bouakkaz, A., Khemis, R., Bounded positive solutions of an iterative three-point boundary-value problem with integral boundary condtions, Journal of Applied Mathematics and Computing, 65 (2021), 597-610. · Zbl 1486.34126
[8] Galvis, J., Rojas, E.M., Sinitsyn, A.V., Existence of positive solutions of a nonlinear second-order boundary value problem with integral boundary conditions, Electron. J. Differential Equations, 2015(236) (2015), 1-7. · Zbl 1331.34037
[9] Guo, L., Sun, J., Zhao, Y., Existence of positive solutions for nonlinear third-order three-point boundary value problems, Nonlinear Anal., 68 (2008), 3151-3158. · Zbl 1141.34310
[10] Haddouchi, F., A note on existence results for a nonlinear fourth-order integral boundary value problem, arXiv:1711.07079v1 [math.CA] 19 Nov 2017. · Zbl 1458.34047
[11] Haddouchi, F., Guendouz, C., Benaicha, S., Existence and multiplicity of positive solutions to a fourthe-order multi-point boundary value problem, arXiv:1908.08598v1 [math.CA] 22 Aug 2019. · Zbl 1474.34170
[12] Kendre, S.D., Kharat, V.V., Narute, R., On existence of solution for iterative integrodifferential equations, Nonlinear Analysis and Differential Equations, 3 (2015), 123-131. · Zbl 1343.45008
[13] Liu, X., Ma, D., The existence of positive solution for a third-order two-point boundary value problem with integral boundary conditions, Scientific Journal of Mathematics Research, 4(1) (2014), 1-7.
[14] Mansouri, B., Ardjouni, A., Djoudi, A., Periodicity and continuous dependence in iterative differential equations, Rendiconti del Circolo Matematico di Palermo Series 2, 69(2) (2020), 561-576. · Zbl 1453.34089
[15] Prasad, K.R., Rashmita, M., Sreedhar, N., Solvability of higher order three-point iterative systems, Ufa Mathematical Journal 12(3) (2020), 107-122. · Zbl 1463.34100
[16] Si, J.G., Wang, X.P., Analytic solutions of a second-order iterative functional differential equation, Computers and Mathematics with Applications, 43 (2002), 81-90. · Zbl 1008.34059
[17] Smart, D.R., Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980. · Zbl 0427.47036
[18] Wang, P., Si, J.G., Analytic solutions of an iterative functional differential equation, Journal of Mathematical Analysis and Applications, 262 (2001), 490-498. · Zbl 1001.34055
[19] Yang, Z., Wang, X., Li, H., Positive solutions for a system of second-order quasilinear boundary value problems, Nonlinear Analysis, 195 (2020), 111749. · Zbl 1436.34020
[20] Zhao, H.Y., Liu, J., Periodic solutions of an iterative functional differential equation with variable coefficients, Math. Methods Appl. Sci., 40 (2017), 286-292. · Zbl 1356.34071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.