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Topological Methods in Nonlinear Analysis

On doubly nonlocal $p$-fractional coupled elliptic system
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  • On doubly nonlocal $p$-fractional coupled elliptic system
  1. Strona domowa /
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  3. Vol 51, No 2 (June 2018) /
  4. Articles

On doubly nonlocal $p$-fractional coupled elliptic system

Autor

  • Tuhina Mukherjee
  • Konijeti Sreenadh

Słowa kluczowe

p-fractional Laplacian, Choquard equation, Nehari manifold

Abstrakt

We study the following nonlinear system with perturbations involving $p$-fractional Laplacian: \begin{equation} \begin{cases} (-\Delta)^s_p u+ a_1(x)u|u|^{p-2} = \alpha(|x|^{-\mu}*|u|^q)|u|^{q-2}u\\ \hskip 2.5 cm + \beta (|x|^{-\mu}*|v|^q)|u|^{q-2}u+ f_1(x)&\text{in } \mathbb R^n, \\ (-\Delta)^s_p v+ a_2(x)v|v|^{p-2} = \gamma(|x|^{-\mu}*|v|^q)|v|^{q-2}v \\ \hskip 2.5cm + \beta (|x|^{-\mu}*|u|^q)|v|^{q-2}v+ f_2(x)& \text{in } \mathbb R^n, \end{cases} \tag{P} \end{equation} where $n> sp$, $0< s< 1$, $p\geq2$, $\mu \in (0,n)$, ${p}( 2-{\mu}/{n})/2 < q < {p^*_s}( 2-{\mu}/{n})/2$, $\alpha,\beta,\gamma > 0$, $0< a_i \in C(\mathbb R^n, \mathbb R)$, $i=1,2$ and $f_1,f_2\colon \mathbb R^n \to \mathbb R$ are perturbations. We show existence of at least two nontrivial solutions for (P) using Nehari manifold and minimax methods.

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2018-05-21

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MUKHERJEE, Tuhina & SREENADH, Konijeti. On doubly nonlocal $p$-fractional coupled elliptic system. Topological Methods in Nonlinear Analysis [online]. 21 maj 2018, T. 51, nr 2, s. 609–636. [udostępniono 7.7.2025].
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