Affiliations: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile. E-mail: [email protected] | Departamento de Matemática, Universidad Técnica Fedrico Santa María, Valparaíso, Chile. E-mail: [email protected]
Note: [] Corresponding author: Patricio Felmer, Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile. E-mail: [email protected].
Abstract: In this article we study existence of boundary blow up solutions for some fractional elliptic equations including (−Δ)αu+up=f in Ω, u=g on Ωc, lim x∈Ω,x→∂Ωu(x)=∞, where Ω is a bounded domain of class C2, α∈(0,1) and the functions f :Ω→R and g :RN\Ω−→R are continuous. We obtain existence of a solution u when the boundary value g blows up at the boundary and we get explosion rate for u under an additional assumption on the rate of explosion of g. Our results are extended for an ample class of elliptic fractional nonlinear operators of Isaacs type.
