Limiting Dynamics of Stochastic p(x)-Laplace Equation with Nonstandard Growth Driven by Pure Jump Noise

• Jiangwei Zhang ^[1] ; Yuhang Wu ^[1] ; Jianhua Huang ^[1]
  1. [1] National University of Defense Technology

     National University of Defense Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
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  • This paper is concerned with the limiting dynamical behavior of solutions for stochastic p(x)-Laplace equation with nonstandard growth condition (NSGC) driven by pure jump noise. Since the presence of variable exponents makes the system distinct from SPDEs with locally monotone coefficients driven by pure jump noise, rendering some existing methods inapplicable directly. To address this, the sufficient conditions on the variable exponents and nonlinearities are established. Based on this, we first prove the existence and uniqueness of solutions of such system, and then we demonstrate that themean random dynamical system associated with stochastic p(x)-Laplace equation, featuring NSGC and small jump noise, possesses a unique weak pullback mean random attractor. Furthermore, we establish the irreducibility of stochastic p(x)-Laplace equation with NSGC driven by pure jump noise. Finally, we prove the existence of invariant measures and obtain the ergodicity via the irreducible result.