Multiple Nontrivial Solutions for a Nonlocal Problem with Sublinear Nonlinearity

Abstract

In this paper, we study the following nonlocal problem −a−b∫Ω ∇u2dxΔu=λu+fxup−2u,x∈Ω,u=0,x∈∂Ω, where a,b>0 are constants, 10, f∈L∞Ω is a positive function, and Ω is a smooth bounded domain in ℝN with N≥3. By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided f∞ is small enough.