Abstract

This paper presents several sufficient conditions for the existence of at least three weak solutions for the following Kirchhoff-type second-order impulsive differential equation

where λ and µ are referred to as two control parameters and is an L² -Carathéodory function. Our technical approach is based on variational methods. The main results are also demonstrated with examples.

中文翻译：

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半线上基尔霍夫型二阶脉冲微分方程的多重解

摘要

本文提出了以下基尔霍夫型二阶脉冲微分方程至少存在三个弱解的几个充分条件

其中 λ 和µ被称为两个控制参数并且是L ² -Carathéodory 函数。我们的技术方法是基于变分方法。主要结果也用例子来证明。