Existence and multiplicity of solutions for second-order impulsive differential equations with Dirichlet problems

Abstract In this paper, we consider the existence and the multiplicity of solutions for second-order impulsive differential equations with Dirichlet boundary conditions, some new existence results are obtained by critical point theory. Our results further improve some existing results.

[1]  X. H. Tang,et al.  New existence and multiplicity of solutions for some Dirichlet problems with impulsive effects , 2012, Math. Comput. Model..

[2]  Eun Kyoung Lee,et al.  Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations , 2004, Appl. Math. Comput..

[3]  W. Ge,et al.  APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS , 2008, Proceedings of the Edinburgh Mathematical Society.

[4]  Liu Yang,et al.  The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method , 2010 .

[5]  Manuel del Pino,et al.  A homotopic deformation along p of a Leray-Schauder degree result and existence for (¦u′¦p − 2u′)′ + ƒ(t, u) = 0, u(0) = u(T) = 0, p > 1 , 1989 .

[6]  Ravi P. Agarwal,et al.  Multiple nonnegative solutions for second order impulsive differential equations , 2000, Appl. Math. Comput..

[7]  Yongkun Li,et al.  Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects , 2009 .

[8]  Weigao Ge,et al.  Calculus of variations for a boundary value problem of differential system on the half line , 2009, Comput. Math. Appl..

[9]  A. N. Sesekin,et al.  Dynamic Impulse Systems , 1997 .

[10]  P. Rabinowitz.  Minimax methods in critical point theory with applications to differential equations , 1986 .

[11]  Xianhua Tang,et al.  Infinitely many homoclinic orbits for Hamiltonian systems with indefinite sign subquadratic potentia , 2011 .

[12]  Xiaoyan Lin,et al.  Existence of infinitely many homoclinic orbits in Hamiltonian systems , 2011, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[13]  Rong Yuan,et al.  An application of variational methods to Dirichlet boundary value problem with impulses , 2010 .

[14]  Periodic Solutions for an Ordinary P-Laplacian System , 2011 .

[15]  J. Mawhin,et al.  Critical Point Theory and Hamiltonian Systems , 1989 .

[16]  Xianhua Tang,et al.  INFINITELY MANY HOMOCLINIC ORBITS OF SECOND-ORDER $p$-LAPLACIAN SYSTEMS , 2013 .

[17]  Yongkun Li,et al.  Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects , 2010 .

[18]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[19]  Kaimin Teng,et al.  Existence of solution to boundary value problem for impulsive differential equations , 2010 .

[20]  D. O’Regan,et al.  Variational approach to impulsive differential equations , 2009 .

[21]  Daqing Jiang,et al.  Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations , 2006 .

[22]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.