Multiplicity Results for Second Order Impulsive Differential Equations via Variational Methods

• 作者: Huanhuan Wang Dan Lu Huiqin Lu
• 来源期刊: 工程(英文)(1947-3931)
• 学科: 数学
• 关键词: Impulsive Differential Equation Sign-Changing Solution Critical Point Theory Variational Method
• 年，卷（期）: 2021,（2）
• 页码范围: 82-93
• 页数: 12页
• 分类号: O17

摘要

In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.