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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04994 |
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Table of Contents:
- This paper deals with the following nonlocal system of equations: \begin{align}\tag{$\mathcal S$}\label{MAT1} (-Δ_p)^s u = \fracα{p_s^*}|u|^{α-2}u|v|^β+f(x) \text{ in } \mathbb{R}^{d}, \, (-Δ_p)^s v = \fracβ{p_s^*}|v|^{β-2}v|u|^α+g(x) \text{ in } \mathbb{R}^{d},\; u,v >0 \mbox{ in } \mathbb{R}^{d}, \end{align} where $0<s<1<p< \infty$, $d>sp$, $α,β>1$, $α+β=\frac{dp}{d-sp}$, and $f,g$ are nontrivial nonnegative functionals in the dual space of $\mathcal{D}^{s,p}(\mathbb{R}^{d})$. The primary objective of this paper is to present a global compactness result that offers a complete characterization of the Palais-Smale sequences of the energy functional associated with \eqref{MAT1}. Using this characterization, within a certain range of $s$, we establish the existence of a solution with negative energy for \eqref{MAT1} when $\ker(f)=\ker(g)$.