Multiplicity Results for the Fractional Laplacian in Expanding Domains
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.
How to cite this document
Figueiredo, Giovany M.; Pimenta, Marcos T. O.; Siciliano, Gaetano. Multiplicity Results for the Fractional Laplacian in Expanding Domains. Mediterranean Journal of Mathematics, v. 15, n. 3, 2018. Available at: <http://hdl.handle.net/11449/176393>.
Keywords
Language
English
Collections
