Abstract
In this paper, a class of fourth-order impulsive differential equations depending on two control parameters is investigated. The existence and multiplicity of solutions are obtained by means of the variational methods and the critical point theory. Finally, an example which supports our theoretical results is also presented.
Highlights
1 Introduction In this paper we will investigate the existence of infinitely many solutions for the following Sturm-Liouville boundary value problem: u(iv)(t) – u (t) + u(t) = λf t, u(t) + μg t, u(t), t = tj, a.e. t ∈ [, T], ( . )
We refer to the impulsive problems ( . )-( . ) as (IP)
Among the papers where impulsive differential equations are investigated by using variational methods, most are for a second-order differential equation, whereas the ones for a fourth-order are mostly about Dirichlet boundary conditions and Neumann boundary conditions
Summary
1 Introduction In this paper we will investigate the existence of infinitely many solutions for the following Sturm-Liouville boundary value problem: u(iv)(t) – u (t) + u(t) = λf t, u(t) + μg t, u(t) , t = tj, a.e. t ∈ [ , T], Zhao et al Boundary Value Problems (2015) 2015:150 existence and multiplicity of solutions of impulsive problems by using variational methods and critical point theory. A function u ∈ X is said to be a weak solution of (IP) if u satisfies One infers that the critical points of the functional Eλ,μ are the weak solutions of (IP).
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