APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

Yu Tian; Weigao Ge

doi:10.1017/S0013091506001532

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we investigate the existence of positive solutions to a second-order Sturm–Liouville boundary-value problem with impulsive effects. The ideas involve differential inequalities and variational methods.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Sun, Juntao and Chen, Haibo 2009. Variational Method to the Impulsive Equation with Neumann Boundary Conditions. Boundary Value Problems, Vol. 2009, Issue. , p. 1.

Tian, Yu Ji, Dehong and Ge, Weigao 2009. Existence and nonexistence results of impulsive first-order problem with integral boundary condition. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 3-4, p. 1250.

Tian, Yu Ge, Weigao and Yang, Dianwu 2009. Existence results for second-order system with impulse effects via variational methods. Journal of Applied Mathematics and Computing, Vol. 31, Issue. 1-2, p. 255.

Tian, Yu Wang, Jun and Ge, Weigao 2009. VARIATIONAL METHODS TO MIXED BOUNDARY VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH A PARAMETER. Taiwanese Journal of Mathematics, Vol. 13, Issue. 4,

Zhou, Jianwen and Li, Yongkun 2009. Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects. Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issue. 7-8, p. 2856.

Sun, Juntao Chen, Haibo and Yang, Liu 2010. The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, Issue. 2, p. 440.

Zhi, Guizhen Zhao, Liang Chen, Guangxia Wang, Shujuan and Zhang, Qihu 2010. Existence of Solutions for Weighted p(r)-Laplacian Impulsive Integro-Differential System Periodic-Like Boundary Value Problems. Journal of Inequalities and Applications, Vol. 2010, Issue. , p. 1.

Zhou, Jianwen and Li, Yongkun 2010. Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects. Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, Issue. 3-4, p. 1594.

Sun, Juntao Chen, Haibo Nieto, Juan J. and Otero-Novoa, Mario 2010. The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects. Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, Issue. 12, p. 4575.

Tian, Yu and Ge, Weigao 2010. Variational methods to Sturm–Liouville boundary value problem for impulsive differential equations. Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, Issue. 1, p. 277.

Heidarkhani, Shapour and Tian, Yu 2010. Multiplicity results for a class of gradient systems depending on two parameters. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, Issue. 2, p. 547.

Sun, Juntao and Chen, Haibo 2010. Multiplicity of solutions for a class of impulsive differential equations with Dirichlet boundary conditions via variant fountain theorems. Nonlinear Analysis: Real World Applications, Vol. 11, Issue. 5, p. 4062.

Zhang, Ziheng and Yuan, Rong 2010. An application of variational methods to Dirichlet boundary value problem with impulses. Nonlinear Analysis: Real World Applications, Vol. 11, Issue. 1, p. 155.

Tian, Yu and Ge, Weigao 2010. Multiple Positive Solutions of Second-Order Sturm-Liouville Boundary Value Problems for Impulsive Differential Equations. Rocky Mountain Journal of Mathematics, Vol. 40, Issue. 2,

Teng, Kaimin and Zhang, Chao 2010. Existence of solution to boundary value problem for impulsive differential equations. Nonlinear Analysis: Real World Applications, Vol. 11, Issue. 5, p. 4431.

Wang, Libo and Pei, Minghe 2011. Infinitely many solutions of a Sturm-Liouville system with impulses. Journal of Applied Mathematics and Computing, Vol. 35, Issue. 1-2, p. 577.

Zhang, Li Huang, Xiankai Ge, Weigao and El-Sayed, A. M. 2011. Positive Solutions of Sturm‐Liouville Boundary Value Problems in Presence of Upper and Lower Solutions. International Journal of Differential Equations, Vol. 2011, Issue. 1,

Tian, Yu and Ge, Weigao 2011. Multiple solutions of Sturm–Liouville boundary value problem via lower and upper solutions and variational methods. Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, Issue. 17, p. 6733.

Liu, Zhisu Chen, Haibo and Zhou, Tiejun 2011. Variational methods to the second-order impulsive differential equation with Dirichlet boundary value problem. Computers & Mathematics with Applications, Vol. 61, Issue. 6, p. 1687.

Yang, Liu Chen, Haibo and Schechter, Martin D. 2011. Existence and Multiplicity of Periodic Solutions Generated by Impulses. Abstract and Applied Analysis, Vol. 2011, Issue. 1,

Download full list

Article contents

APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

Abstract

Keywords

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests