Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains

Abstract

We investigate the existence and the multiplicity of positive solutions for the semilinear elliptic equation − u + u = Q (x)|u| p−2 u in exterior domain which is very close to R N . The potential Q (x) tends to positive constant at infinity and may change sign.

Existence and multiplicity of solutions for a non-linear Schrödinger equation with non-local regional diffusion

“…Before concluding this introduction, we would like point out that in the proof of Theorem [24]. In the above papers the authors have studied the existence and multiplicity of solution for problems involving the Laplacian operator.…”

“…Before concluding this introduction, we would like point out that in the proof of Theorem 1.1 we adapt some ideas explored in Alves, Carrião & Miyagaki [2], Cao & Noussair [4], Cao & Zhou [5], Hsu, Lin & Hu [22], Lin [23] and Hu & Tang [24]. In the above papers the authors have studied the existence and multiplicity of solution for problems involving the Laplacian operator.…”