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Zhang, Xingqiu

Computation of positive solutions for nonlinear impulsive integral boundary value problems with \(p\)-Laplacian on infinite intervals. (English) Zbl 1266.65135

Abstr. Appl. Anal. 2013, Article ID 708281, 13 p. (2013).
Summary: This paper deals with the existence and iteration of positive solutions for nonlinear second-order impulsive integral boundary value problems with \(p\)-Laplacian on infinite intervals. Our approach is based on the monotone iterative technique.

Cited in 1 Document

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34A37 Ordinary differential equations with impulses

Keywords:

positive solutions; nonlinear second-order impulsive integral boundary value problems; \(p\)-Laplacian; infinite intervals; monotone iterative technique
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References:

[1] Lakshmikantham, V.; Baĭnov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations. Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics, 6, xii+273 (1989), Teaneck, NJ, USA: World Scientific Publishing, Teaneck, NJ, USA · Zbl 0719.34002
[2] Baĭnov, D. D.; Simeonov, P. S., Systems with Impulse Effect: Stability, Theory and Application. Systems with Impulse Effect: Stability, Theory and Application, Ellis Horwood Series: Mathematics and its Applications, 255 (1989), Chichester, UK: Ellis Horwood, Chichester, UK · Zbl 0683.34032
[3] Samoĭlenko, A. M.; Perestyuk, N. A., Impulsive Differential Equations. Impulsive Differential Equations, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 14, x+462 (1995), River Edge, NJ, USA: World Scientific Publishing, River Edge, NJ, USA · Zbl 0837.34003 · doi:10.1142/9789812798664
[4] Agarwal, R. P.; O’Regan, D., Infinite Interval Problems for Differential, Difference and Integral Equations, x+341 (2001), Dordrecht, The Netherland: Kluwer Academic Publishers, Dordrecht, The Netherland · Zbl 0988.34002 · doi:10.1007/978-94-010-0718-4
[5] Chen, S. Z.; Zhang, Y., Singular boundary value problems on a half-line, Journal of Mathematical Analysis and Applications, 195, 2, 449-468 (1995) · Zbl 0852.34019 · doi:10.1006/jmaa.1995.1367
[6] Liu, X., Solutions of impulsive boundary value problems on the half-line, Journal of Mathematical Analysis and Applications, 222, 2, 411-430 (1998) · Zbl 0912.34021 · doi:10.1006/jmaa.1997.5908
[7] Zima, M., On positive solutions of boundary value problems on the half-line, Journal of Mathematical Analysis and Applications, 259, 1, 127-136 (2001) · Zbl 1003.34024 · doi:10.1006/jmaa.2000.7399
[8] Li, J.; Nieto, J. J., Existence of positive solutions for multipoint boundary value problem on the half-line with impulses, Boundary Value Problems, 2009 (2009) · Zbl 1177.34041
[9] Karakostas, G. L.; Tsamatos, P. Ch., Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems, Electronic Journal of Differential Equations, 30, 1-17 (2002) · Zbl 0998.45004
[10] Karakostas, G. L.; Tsamatos, P. Ch., Existence of multiple positive solutions for a nonlocal boundary value problem, Topological Methods in Nonlinear Analysis, 19, 1, 109-121 (2002) · Zbl 1071.34023
[11] Webb, J. R. L.; Infante, G., Positive solutions of nonlocal boundary value problems: a unified approach, Journal of the London Mathematical Society, 74, 3, 673-693 (2006) · Zbl 1115.34028 · doi:10.1112/S0024610706023179
[12] Webb, J. R. L.; Infante, G., Positive solutions of nonlocal boundary value problems involving integral conditions, Nonlinear Differential Equations and Applications, 15, 1-2, 45-67 (2008) · Zbl 1148.34021 · doi:10.1007/s00030-007-4067-7
[13] Yang, Z., Existence and nonexistence results for positive solutions of an integral boundary value problem, Nonlinear Analysis. Theory, Methods & Applications A, 65, 8, 1489-1511 (2006) · Zbl 1104.34017 · doi:10.1016/j.na.2005.10.025
[14] Yang, Z., Positive solutions of a second-order integral boundary value problem, Journal of Mathematical Analysis and Applications, 321, 2, 751-765 (2006) · Zbl 1106.34014 · doi:10.1016/j.jmaa.2005.09.002
[15] Feng, M., Existence of symmetric positive solutions for a boundary value problem with integral boundary conditions, Applied Mathematics Letters, 24, 8, 1419-1427 (2011) · Zbl 1221.34062 · doi:10.1016/j.aml.2011.03.023
[16] Feng, M.; Zhang, X.; Ge, W., New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions, Boundary Value Problems, 2011 (2011) · Zbl 1214.34005 · doi:10.1155/2011/720702
[17] Ahmad, B.; Alsaedi, A.; Alghamdi, B. S., Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Nonlinear Analysis. Real World Applications, 9, 4, 1727-1740 (2008) · Zbl 1154.34311 · doi:10.1016/j.nonrwa.2007.05.005
[18] Feng, M.; Liu, X.; Feng, H., The existence of positive solution to a nonlinear fractional differential equation with integral boundary conditions, Advances in Difference Equations, 2011 (2011) · Zbl 1219.34009
[19] Kang, P.; Wei, Z.; Xu, J., Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces, Applied Mathematics and Computation, 206, 1, 245-256 (2008) · Zbl 1169.34043 · doi:10.1016/j.amc.2008.09.010
[20] Zhang, X.; Ge, W., Symmetric positive solutions of boundary value problems with integral boundary conditions, Applied Mathematics and Computation, 219, 8, 3553-3564 (2012) · Zbl 1311.34054 · doi:10.1016/j.amc.2012.09.037
[21] Zhang, X.; Yang, X.; Feng, M., Minimal nonnegative solution of nonlinear impulsive differential equations on infinite interval, Boundary Value Problems, 2011 (2011) · Zbl 1209.34036
[22] Guo, D., Existence of positive solutions for \(n\) th-order nonlinear impulsive singular integro-differential equations in Banach spaces, Nonlinear Analysis. Theory, Methods & Applications A, 68, 9, 2727-2740 (2008) · Zbl 1140.45017 · doi:10.1016/j.na.2007.02.019
[23] Liu, Y., Existence and unboundedness of positive solutions for singular boundary value problems on half-line, Applied Mathematics and Computation, 144, 2-3, 543-556 (2003) · Zbl 1036.34027 · doi:10.1016/S0096-3003(02)00431-9
[24] Liu, Y., Boundary value problems for second order differential equations on unbounded domains in a Banach space, Applied Mathematics and Computation, 135, 2-3, 569-583 (2003) · Zbl 1035.34015 · doi:10.1016/S0096-3003(02)00070-X
[25] Yan, B.; O’Regan, D.; Agarwal, R. P., Unbounded solutions for singular boundary value problems on the semi-infinite interval: upper and lower solutions and multiplicity, Journal of Computational and Applied Mathematics, 197, 2, 365-386 (2006) · Zbl 1116.34016 · doi:10.1016/j.cam.2005.11.010
[26] Yan, B.; Liu, Y., Unbounded solutions of the singular boundary value problems for second order differential equations on the half-line, Applied Mathematics and Computation, 147, 3, 629-644 (2004) · Zbl 1045.34009 · doi:10.1016/S0096-3003(02)00801-9
[27] Lian, H.; Pang, H.; Ge, W., Triple positive solutions for boundary value problems on infinite intervals, Nonlinear Analysis. Theory, Methods & Applications A, 67, 7, 2199-2207 (2007) · Zbl 1128.34011 · doi:10.1016/j.na.2006.09.016
[28] Liang, S.; Zhang, J., The existence of countably many positive solutions for some nonlinear three-point boundary problems on the half-line, Nonlinear Analysis. Theory, Methods & Applications A, 70, 9, 3127-3139 (2009) · Zbl 1166.34304 · doi:10.1016/j.na.2008.04.016
[29] Liu, L.; Liu, Z.; Wu, Y., Infinite boundary value problems for \(n\) th-order nonlinear impulsive integro-differential equations in Banach spaces, Nonlinear Analysis. Theory, Methods & Applications A, 67, 9, 2670-2679 (2007) · Zbl 1124.45008 · doi:10.1016/j.na.2006.09.031
[30] Ma, D.-X.; Du, Z.-J.; Ge, W.-G., Existence and iteration of monotone positive solutions for multipoint boundary value problem with \(p\)-Laplacian operator, Computers & Mathematics with Applications, 50, 5-6, 729-739 (2005) · Zbl 1095.34009 · doi:10.1016/j.camwa.2005.04.016
[31] Sun, B.; Zhao, J.; Yang, P.; Ge, W., Successive iteration and positive solutions for a third-order multipoint generalized right-focal boundary value problem with \(p\)-Laplacian, Nonlinear Analysis. Theory, Methods & Applications A, 70, 1, 220-230 (2009) · Zbl 1161.34318 · doi:10.1016/j.na.2007.11.048
[32] Sun, B.; Yang, A.; Ge, W., Successive iteration and positive solutions for some second-order three-point \(p\)-Laplacian boundary value problems, Mathematical and Computer Modelling, 50, 3-4, 344-350 (2009) · Zbl 1185.34030 · doi:10.1016/j.mcm.2008.08.024
[33] Liu, Y. S., A boundary value problem for a second-order differential equation on an unbounded domain, Acta Analysis Functionalis Applicata, 4, 3, 211-216 (2002) · Zbl 1038.34030
[34] Corduneanu, C., Integral Equations and Stability of Feedback Systems, ix+238 (1973), New York, NY, USA: Academic Press, New York, NY, USA · Zbl 0273.45001
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