Existence and multiplicity of standing wave solutions for perturbed fractional p -Laplacian systems involving critical exponents

AIMS Mathematics

article

Shulin Zhang¹ 

[1] School of Mathematics, China University of Mining and Technology;School of Mathematics

关键词: perturbed fractional p -Laplacian systems;    critical growth;    variational methods;    standing wave solutions;   

DOI  :  10.3934/math.2023048

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we investigate the existence of standing wave solutions to the following perturbed fractional p -Laplacian systems with critical nonlinearity$ \begin{equation*} \left\{ \begin{aligned} &\varepsilon^{ps}(-\Delta)^{s}_{p}u + V(x)|u|^{p-2}u = K(x)|u|^{p^{*}_{s}-2}u + F_{u}(x, u, v), \; x\in \mathbb{R}^{N}, \\ &\varepsilon^{ps}(-\Delta)^{s}_{p}v + V(x)|v|^{p-2}v = K(x)|v|^{p^{*}_{s}-2}v + F_{v}(x, u, v), \; x\in \mathbb{R}^{N}. \end{aligned} \right. \end{equation*} $Under some proper conditions, we obtain the existence of standing wave solutions $ (u_{\varepsilon}, v_{\varepsilon}) $ which tend to the trivial solutions as $ \varepsilon\rightarrow 0 $. Moreover, we get $ m $ pairs of solutions for the above system under some extra assumptions. Our results improve and supplement some existing relevant results.

【 授权许可】

CC BY