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.
Citation: Shulin Zhang. Existence and multiplicity of standing wave solutions for perturbed fractional p-Laplacian systems involving critical exponents[J]. AIMS Mathematics, 2023, 8(1): 997-1013. doi: 10.3934/math.2023048
In this paper, we investigate the existence of standing wave solutions to the following perturbed fractional
$ \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.
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Shulin Zhang. Existence and multiplicity of standing wave solutions for perturbed fractional p-Laplacian systems involving critical exponents[J]. AIMS Mathematics, 2023, 8(1): 997-1013. doi: 10.3934/math.2023048
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