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Guo, D., Sun, J. and Liu, Z. (1995) Functional Methods in Nonlinear Ordinary Differential Equations. Shandong Science and Technology Press, Jinan. (in Chinese)

has been cited by the following article:

• TITLE: Multiplicity Results for Second Order Impulsive Differential Equations via Variational Methods

  AUTHORS: Huanhuan Wang, Dan Lu, Huiqin Lu

  KEYWORDS: Impulsive Differential Equation, Sign-Changing Solution, Critical Point Theory, Variational Method

  JOURNAL NAME: Engineering, Vol.13 No.2, February 25, 2021

  ABSTRACT: In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of 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.