Existence of solutions for first-order Hamiltonian stochastic impulsive differential equations with Dirichlet boundary conditions

2021/05/19 by Yu Guo, Xiao-Bao Shu, Guo, Yu +4
Mathematics · #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR) #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.2105.09101

arxiv created 2021/05/19 · openalex publication_date 2021/05/19 · arxiv updated 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the sufficient conditions for the existence of solutions of first-order Hamiltonian stochastic impulsive differential equations under Dirichlet boundary value conditions. By using the variational method, we first obtain the corresponding energy functional. And by using Legendre transformation, we obtain the conjugation of the functional. Then the existence of critical point is obtained by mountain pass lemma. Finally, we assert that the critical point of the energy functional is the mild solution of the first order Hamiltonian stochastic impulsive differential equation.Finally, an example are presented to illustrate the feasibility and effectiveness of our results.

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