2023/10/30 by Ángel Crespo‐Blanco, Crespo-Blanco, Ángel, Leszek Gasiński +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2310.20013
openalex publication_date 2023/10/30 · openalex created_date 2023/11/02 · openalex updated_date 2026/08/01
In this paper we study the following nonlocal Dirichlet equation of double phase type -ψ [ ∫Ω ( (|∇ u |p)/(p) + μ(x) (|∇ u|q)/(q)) d x] G(u) = f(x,u) in Ω, u = 0 on ∂Ω, where G is the double phase operator given by G(u)=div (|∇ u|p-2∇ u + μ(x) |∇ u|q-2∇ u ) u∈ W1,H0(Ω), Ω⊆ ℝN, N≥ 2, is a bounded domain with Lipschitz boundary ∂Ω, 10 and ϑ ≥ 1, and f\colonΩ×ℝ→ℝ is a Carathéodory function that grows superlinearly and subcritically. We prove the existence of two constant sign solutions (one is positive, the other one negative) and of a sign-changing solution which turns out to be a least energy sign-changing solution of the problem above. Our proofs are based on variational tools in combination with the quantitative deformation lemma and the Poincaré-Miranda existence theorem.