A multiplicity theorem for a class of nonlocal elliptic equations involving even nonlinearities

2026/07/20 by Biagio Ricceri
#math.AP

paper · pdf

Abstract

In this paper, on a bounded domain Ω⊂ \bf Rⁿ, we consider a nonlocal problem of the type \cases-Δu=Q(u,λ)f(u) in Ω \cr \cr u=0 on ∂Ω\cr where Q:H¹₀(Ω)× \bf R→ \bf R, proving, under suitable assumptions, the existence of at least three weak solutions for each λ running in a suitable interval.

Related

• A multiplicity result for nonlocal problems involving nonlinearities with bounded primitive
• Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition
• Multiplicity of solutions for mixed local-nonlocal elliptic equations with singular nonlinearity
• Multiplicity results for non-local operators of elliptic type
• A Global multiplicity result for a very singular critical nonlocal equation