Existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions-Reference-Cited by-同舟云学术

Existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions

Published:2022 Issue:5 Volume:7 Page:7685-7705
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Wang Song, ,Shu Xiao-Bao,Shu Linxin

Abstract

<abstract><p>In this paper, we study sufficient conditions for the existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions. By using variational method we first obtain the corresponding energy functional. Then the existence of critical points are obtained by using Mountain pass lemma and Minimax principle. Finally we assert the critical point of enery functional is the mild solution of damped random impulsive differential equations.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference39 articles.

1. T. E. Carter, Optimal impulsive space trajectories based on linear equations, J. Optim. Theory Appl. 70 (1991), 277–297. https://doi.org/10.1007/BF00940627

2. T. E. Carter, Necessary and sufficient conditions for optimal impulsive rendezvous with linear equations of motion, Dynam. Control., 10 (2000), 219–227.

3. P. Chen, X. H. Tang, Existence and multiplicity of solutions for second-order impulsive differential equations with Dirichlet problems, Appl. Math. Comput., 218 (2012), 11775–11789. https://doi.org/10.1016/j.amc.2012.05.027

4. S. Deng, X. Shu, J. Mao, Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Monch fixed point, J. Math. Anal. Appl., 467 (2018), 398–420. https://doi.org/10.1016/j.jmaa.2018.07.002

5. W. Ding, D. B. Qian, Periodic solutions for sublinear systems via variational approach, Nonlinear Anal-Real., 11 (2010), 2603–2609. https://doi.org/10.1016/j.nonrwa.2009.09.007

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence and Multiplicity of Mild Solutions for First-Order Hamilton Random Impulsive Differential Equations with Dirichlet Boundary Conditions;Qualitative Theory of Dynamical Systems;2023-02-08

2. On the variational principle and applications for a class of damped vibration systems with a small forcing term;AIMS Mathematics;2023

3. A study on the mild solution of special random impulsive fractional differential equations;Mathematics in Applied Sciences and Engineering;2022-12-14

4. HJB equation for optimal control system with random impulses;Optimization;2022-12-07