Three Solutions for a Perturbed Integral Equation with Homogeneous Dirichlet Condition

Abstract:

We consider the integral equation (Formula presented), with homogeneous Dirichlet condition on a bounded Lipschitz domain of R^N where λ, µ ∈ R, p ≥ 2, s ∈]0, 1[, N > ps, f, g: R^N → R are Carathéodory functions with subcritical growth and −L^p denotes a class of operators that includes (−∆)^s<inf>p</inf>, the fractional p-Laplacian. Here µg represents a small perturbation of λf. Applying an abstract critical point theorem due to Ricceri, a variational setting developed by Xiang et al. and a Minti-Browder’s theorem, we prove the existence of three weak solutions.

Año de publicación:

2025

Keywords:

• Critical Points
• Integral elliptic equation
• Variational methods

Fuente:

scopus