We take up in this paper the existence of positive continuous solutions for some nonlinear boundary value problems with fractional differential equation based on the fractional Laplacian (− |D ) α 2 associated to the subordinate killed Brownian motion process Z D α in a bounded C 1,1 domain D. Our arguments are based on potential theory tools on Z D α and properties of an appropriate Kato class of functions K α (D).
Abstract.Let Ω be a bounded domain in R n (n ≥ 2) with a smooth boundary ∂Ω. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic systemHere r, s ∈ R, α, β < 1 such that γ := (1 − α)(1 − β) − rs > 0 and the functions ai (i = 1, 2) are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.