Multiplicity Results for the Fractional Laplacian in Expanding Domains
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Abstract
In this paper, we establish a multiplicity result of nontrivial weak solutions for the problem (- Δ) αu+ u= h(u) in Ω λ, u= 0 on ∂Ω λ, where Ω λ= λΩ , Ω is a smooth and bounded domain in RN, N> 2 α, λ is a positive parameter, α∈ (0 , 1) , (- Δ) α is the fractional Laplacian and the nonlinear term h(u) has subcritical growth. We use minimax methods, the Ljusternick–Schnirelmann and Morse theories to get multiplicity results depending on the topology of Ω.
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Fractional Laplacian, Ljusternick–Schnirelmann category, Morse theory, multiplicity of solutions
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English
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Mediterranean Journal of Mathematics, v. 15, n. 3, 2018.
