Multiplicity of solutions for a p-Schrödinger–Kirchhoff-type integro-differential equation

Abstract:

We consider the integro-differential problem (P): -(a+b(∫RN|∇u|pdx)p-1)Δpu+V(x)|u|p-2u=f(x,u),x∈RN,with | u(x) | ⟶ 0 , as | x| ⟶ + ∞. We assume that a, b> 0 , N≥ 2 , 1 < p< N< + ∞, V∈ C (RN) with inf (V) > 0 , and that f: RN× R⟶ R verifies conditions introduced by Duan and Huang. We prove the existence of a non-trivial ground state solution and, by a Ljusternik–Schnirelman scheme, the existence of infinitely many non-trivial solutions.

Año de publicación:

2023

Keywords:

• p-Schrödinger–Kirchhoff-type equation
• Ljusternik–Schnirelman theory
• Critical point theory

Fuente:

scopus