The effect of the domain topology on the number of solutions of fractional Laplace problems
type: Item
instance of: scholarly article
title: The effect of the domain topology on the number of solutions of fractional Laplace problems
zbMATH Open document ID: 1423.35110
author: Giovany M. Figueiredo
author: Giovanni Molica Bisci
author: Raffaella Servadei
published in: Calculus of Variations and Partial Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Boundary value problems for elliptic equations involving fractional operators represent a very active field of research, see the survey of \textit{G. Grubb} [in: Mathematical analysis and applications -- plenary lectures. Papers based on the presentations at the 11th international ISAAC congress, Växjö, Sweden, August 14--18, 2017. Cham: Springer. 51--81 (2018; Zbl 1414.35099)] for a precise setting of the boundary conditions. Here the authors consider the nonlinear equation \[(-\Delta)^s u= (\lambda|u|^p+|u|^q)\,u,\] with $0<s<1$, $\lambda>0$, in a bounded domain $\Omega\subset\mathbb{R}^n$ and discuss in detail multiplicity of solutions under differential assumptions on $p$ an $q$. In particular, the number of the nontrivial solutions is related to the geometric properties of the domain $\Omega$.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6916248
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: semilinear equation
zbMATH Keywords: multiplicity of solutions
MaRDI profile type: Publication
full work available at URL: s00526-018-1382-2
OpenAlex ID: W2808181517
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DOI: 10.1007/S00526-018-1382-2
Wikidata QID: Q129684849
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description: scientific article; zbMATH DE number 6916248