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Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods. (English) Zbl 1251.34046

The authors consider the impulsive boundary value problem

-(p(t)u ' (t)) ' +r(t)u ' (t)+q(t)u(t)=f(t,u(t))fora.e.t[0,T],tt j ,-Δ(p(t j )u ' (t j ))=I j (u(t j )),j=1,,n,u(0)=0,a 1 u(1)+u ' (1)=0,

where 0<t 1 <<t n <1, fC[[0,1]×,], pC 1 [0,1], qC[0,1]. There are obtained multiplicity existence results for this type of BVP. As a main tool, variational methods are used.

MSC:
34B37Boundary value problems for ODE with impulses
58E30Variational principles on infinite-dimensional spaces
References:
[1]Benchohra, M.; Henderson, J.; Ntouyas, S. K.: Impulsive differential equations and inclusions, Impulsive differential equations and inclusions 2 (2006) · Zbl 1130.34003
[2]Zavalishchin, S. T.; Sesekin, A. N.: Dynamic impulse systems: theory and applications, (1997)
[3]Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations, (1995) · Zbl 0837.34003
[4]Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[5]Meng, X.; Li, Z.; Nieto, J. J.: Dynamic analysis of michaelis – menten chemostat-type competition models with time delay and pulse in a polluted environment, J math chem 47, 123-144 (2010) · Zbl 1194.92075 · doi:10.1007/s10910-009-9536-2
[6]Luo, Z.; Nieto, J. J.: New results for the periodic boundary value problem for impulsive integro-differential equations, Nonlinear anal 70, 2248-2260 (2009) · Zbl 1166.45002 · doi:10.1016/j.na.2008.03.004
[7]Yu, H.; Zhong, Sh.; Agarwal, Ravi P.: Mathematics analysis and chaos in an ecological model with an impulsive control strategy, Commun nonlinear sci numer simul 16, 776-786 (2011) · Zbl 1221.37207 · doi:10.1016/j.cnsns.2010.04.017
[8]Zeng, G.; Wang, F.; Nieto, J. J.: Complexity of a delayed predator-prey model with impulsive harvest and Holling-type II functional response, Adv complex syst 11, 77-97 (2008) · Zbl 1168.34052 · doi:10.1142/S0219525908001519
[9]Zhang, H.; Chen, L. S.; Nieto, J. J.: A delayed epidemic model with stage structure and pulses for management strategy, Nonlinear anal: real world appl 9, 1714-1726 (2008) · Zbl 1154.34394 · doi:10.1016/j.nonrwa.2007.05.004
[10]Nieto, J. J.; Rodriguez-Lopez, R.: Boundary value problems for a class of impulsive functional equations, Comput math appl 55, 2715-2731 (2008) · Zbl 1142.34362 · doi:10.1016/j.camwa.2007.10.019
[11]Wang, W. B.; Shen, J. H.; Nieto, J. J.: Permanence periodic solution of predator prey system with Holling type functional response and impulses, Discrete dyn nat soc, 15 (2007) · Zbl 1146.37370 · doi:10.1155/2007/81756
[12]Xia, Y. H.: Global analysis of an impulsive delayed Lotka – Volterra competition system, Commun nonlinear sci numer simul 16, 1597-1616 (2011) · Zbl 1221.34206 · doi:10.1016/j.cnsns.2010.07.014
[13]Sun, J.; Chen, H.; Nieto, J. J.; Otero-Novoa, M.: Multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects, Nonlinear anal TMA 72, 4575-4586 (2010) · Zbl 1198.34036 · doi:10.1016/j.na.2010.02.034
[14]Yan, J.; Zhao, A.; Nieto, J. J.: Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka – Volterra systems, Math comput model 40, 509-518 (2004) · Zbl 1112.34052 · doi:10.1016/j.mcm.2003.12.011
[15]Liu, X.; Willms, A. R.: Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft, Math probl eng 2, 277-299 (1996) · Zbl 0876.93014 · doi:10.1155/S1024123X9600035X
[16]Pasquero, S.: Ideality criterion for unilateral constraints in time-dependent impulsive mechanics, J math phys 46, 112904 (2005) · Zbl 1111.70015 · doi:10.1063/1.2121247
[17]Nieto, J. J.; O’regan, D.: Variational approach to impulsive differential equations, Nonlinear anal 10, 680-690 (2009) · Zbl 1167.34318 · doi:10.1016/j.nonrwa.2007.10.022
[18]Tian, Y.; Ge, W. G.: Variational methods to Sturm – Liouville boundary value problem for impulsive differential equations, Nonlinear anal 72, 277-287 (2010) · Zbl 1191.34038 · doi:10.1016/j.na.2009.06.051
[19]Xiao, J.; Nieto, J. J.: Variational approach to some damped Dirichlet nonlinear impulsive differential equations, J franklin I 348, 369-377 (2011) · Zbl 1228.34048 · doi:10.1016/j.jfranklin.2010.12.003
[20]Tian, Y.; Ge, W. G.: Applications of variational methods to boundary value problem for impulsive differential equations, P Edinburgh math soc 51, 509-527 (2008) · Zbl 1163.34015 · doi:10.1017/S0013091506001532
[21]Nieto, J. J.: Variational formulation of a damped Dirichlet impulsive problem, Appl math lett 23, 940-942 (2010) · Zbl 1197.34041 · doi:10.1016/j.aml.2010.04.015
[22]Mawhin, J.; Willem, M.: Critical point theory and Hamiltonian systems, (1989)
[23]Zeidler, E.: Nonlinear functional analysis and its applications. III: variational methods and optimization, (1985) · Zbl 0583.47051
[24]Rabinowitz, P. H.: Minimax methods in critical point theory with applications to differential equations, CBMS regional conference series in mathematics 65 (1986) · Zbl 0609.58002