Existence results of weak solution to perturbed Kirchhoff type problems for impulsive differential equations, By Mohsen Alimohammady

Research

Title	Existence results of weak solution to perturbed Kirchhoff type problems for impulsive differential equations
Type	Article
Keywords	Impulsive effects; Kirchhoff type problems; Weak solution; Critical points theorems
Journal	Nonlinear Studies
DOI	http://nonlinearstudies.com/index.php/nonlinear/ar
Researchers	Fatemeh Vahedi (First researcher) , Ghasem Alizadeh Afrouzi (Second researcher) , Mohsen Alimohammady (Third researcher)

Abstract

In this paper, using a variational method and some critical points theorems, we show the existence of at least one weak solution for perturbed impulsive fourth-order Kirchhoff type problems. Indeed, using a consequence of the local minimum theorem due Bonanno we investigate the existence of one nontrivial solution for our problem under algebraic conditions on the nonlinear part. A concrete example of an application is then presented.