Bifurcation properties for a class of fractional Laplacian equations in RN

Claudianor O. Alves, Romildo N. de Lima and Alânnio B. Nóbrega

Mathematische Nachrichten, 2018, vol. 291, issue 14-15, 2125-2144

Abstract: This paper concerns with the study of some bifurcation properties for the following class of nonlocal problems P (−Δ)su=λf(x)(u+h(u)),inRN,u(x)>0,forallx∈RN,lim|x|→∞u(x)=0,where N>2s, s∈(0,1), λ>0, f:RN→R is a positive continuous function, h:R→R is a bounded continuous function and (−Δ)su is the fractional Laplacian. The main tools used are the Leray–Shauder degree theory and the global bifurcation result due to Rabinowitz.

Date: 2018
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