Work

Dynamics of the compact almost automorphic solution for a class of stochastic nonlinear differential equations

Year: 2025

Type: article

Abstract: This paper mainly considers the existence of the compact almost automorphic mild solution for a class of stochastic nonlinear differential equations. More specifically, based on $ C_{0} $-semigroup theory, Hölder inequality, Burkholder–Davis–Gundy inequality and Lebesgue dominated convergence theorem, we obtain that the $ K $-mild solution is uniformly continuous and is relatively compact, etc. Combined with the subvariant functional method, we give some sufficient conditions to make sure that there exists at least one minimal $ K $-mild solution; further, if the minimal $ K $-mild solution is unique, then it is compact and almost automorphic. Moreover, we provide an example to illustrate the main presented results.

Source: AIMS Mathematics

DOI: 10.3934/math.2025712

Author: Ping Zhu

Institution: Luoyang Normal University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Natural Science Foundation of Henan Province