Abstract
We consider the integro-differential system \((\textrm{P}_m)\):
where \(x\in {\mathbb {R}}^N\), \(a_k>0\), \(b_k\ge 0\), \(N\ge 2\) and \(1<p<N\), \(u_k \in \textrm{W}^{1,p}({\mathbb {R}}^{N})\), for \(k=1,\ldots ,m\). By \(\partial _{k} F(u_1,\ldots ,u_m),\) it is denoted the k-th partial generalized gradient in the sense of Clarke. The potential \(V\in \textrm{C} \left( {\mathbb {R}}^N \right) \) verifies \(\inf (V)>0\) and a coercivity property introduced by Bartsch et al. The coupling function \(F:{\mathbb {R}}^m\longrightarrow {\mathbb {R}}\) is locally Lipschitz and verifies conditions introduced by Duan and Huang. By applying tools from the non-smooth critical point theory, we prove the existence of a non-trivial mountain pass solution of \((\textrm{P}_m)\).
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Mayorga-Zambrano, J., Narváez-Vaca, D. A non-trivial solution for a p-Schrödinger–Kirchhoff-type integro-differential system by non-smooth techniques. Ann. Funct. Anal. 14, 77 (2023). https://doi.org/10.1007/s43034-023-00299-5
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DOI: https://doi.org/10.1007/s43034-023-00299-5
Keywords
- p-Schrödinger–Kirchhoff-type system
- Non-smooth mountain pass theorem
- Non-smooth critical point theory
- Integro-differential system