Multiplicity results for the fractional laplacian in expanded domains

2015/11/30 by Giovany M. Figueiredo, Figueiredo, G. M., Marcos T. O. Pimenta +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1511.09406

openalex publication_date 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we establish the multiplicity of nontrivial weak solutions for the problem (-Δ)^α u +u= h(u) in Ω_λ, u=0 on ∂Ω_λ, where Ω_λ=λΩ, Ω is a smooth and bounded domain in ℝ^N, N>2α, λ is a positive parameter, α∈ (0,1), (-Δ)^α is the fractional Laplacian and the nonlinear term h(u) has a subcritical growth. We use minimax methods, the Ljusternick-Schnirelmann and Morse theories to get multiplicity result depending on the topology of Ω.

Citations

• Nonlinear equations for fractional Laplacians I: Regularity, maximum\n principles, and Hamiltonian estimates

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• Asymptotic issue for fractional laplacian on long cylinders

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