A non-trivial solution for a p-Schrödinger–Kirchhoff-type integro-differential system by non-smooth techniques

Abstract:

We consider the integro-differential system (P <inf>m</inf>) : -(ak+bk(∫RN|∇uk|pdx)p-1)Δpuk+V(x)|uk|p-2uk=∂kF(u1,…,um), where x∈ R^N , a<inf>k</inf>> 0 , b<inf>k</inf>≥ 0 , N≥ 2 and 1 < p< N , u<inf>k</inf>∈ W ¹^,^p(R^N) , for k= 1 , … , m . By ∂<inf>k</inf>F(u<inf>1</inf>, … , u<inf>m</inf>) , it is denoted the k-th partial generalized gradient in the sense of Clarke. The potential V∈ C (R^N) verifies inf (V) > 0 and a coercivity property introduced by Bartsch et al. The coupling function F: R^m⟶ 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 (P <inf>m</inf>) .

Año de publicación:

2023

Keywords:

• Integro-differential system
• Non-smooth critical point theory
• Non-smooth mountain pass theorem
• p-Schrödinger–Kirchhoff-type system

Fuente:

scopus