Existence and Multiplicity of Mild Solutions for First-Order Hamilton Random Impulsive Differential Equations with Dirichlet Boundary Conditions

Qian-Bao Yin ^[1] ; Yu Guo ^[1] ; Dan Wu ^[1] ; Xiao-Bao Shu ^[1]
1. [1] Hunan University
  
  Hunan University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
Idioma: inglés
Enlaces
- Texto completo
Resumen
- In this paper, we study the sufficient conditions for multiple solutions of first-order Hamiltonian random impulsive differential equations under Dirichlet boundary value conditions. For systems with random impulses, the variational principle with random impulses is constructed, and the energy function is treated by its conjugate action.
  
  Then, the generalized saddle point theorem is used to show that the energy functional has multiple critical points, that is, the first-order Hamiltonian random impulses differential equation has multiple weak solutions. Finally, we give an example to illustrate the feasibility and effectiveness of this method.