A fractional Ambrosetti-Prodi type problem in RN

de Lima R.N.; Torres Ledesma C.E.; Nóbrega A.B. · Journal of Elliptic and Parabolic Equations (2023) · DOI: 10.1007/s41808-022-00201-9

Resumen

In this paper we deal with the existence and non-existence of solutions for the following Ambrosetti-Prodi type problem {(-Δ)su=P(x)(g(u)+f(x))inRN,u∈Ds(RN),lim|x|→+∞u(x)=0,where N> 2 s, s∈ (0 , 1) , P∈ C(RN, R+) , f∈ C1,σ(RN) ∩ L∞(RN) , g∈ C1,σ(R) and (- Δ) su is the fractional Laplacian. The main tools used are the sub-supersolution method and Leray-Schauder topological degree theory.

Instituciones: Universidad Nacional de Trujillo