Open AccessExistence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions
Author(s) -
Song Wang,
AUTHOR_ID,
Xu Shu,
Linxin Shu
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022431
Subject(s) - mathematics , mathematical analysis , boundary value problem , lemma (botany) , minimax , dirichlet distribution , class (philosophy) , dirichlet boundary condition , mathematical optimization , computer science , ecology , poaceae , artificial intelligence , biology
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.