Positive solutions for singular elliptic equations with mixed Dirichlet-Neumann boundary conditions

Abstract

In this paper, we investigate the existence of positive solutions for singular elliptic equations with mixed Dirichlet‐Neumann boundary conditions involving Sobolev‐Hardy critical exponents and Hardy terms by using the concentration compactness principle, the strong maximum principle and the Mountain Pass lemma. We also prove, under complementary conditions, that there is no nontrivial solution if the domain is star‐shaped with respect to the origin.

Positive Radial Solutions for a Class of Semilinear Elliptic Problems Involving Critical Hardy-Sobolev Exponent and Hardy Terms

“…For example, by using the concentration compactness principle, the strong maximum principle and the Mountain Pass lemma, Li et al [3] had obtained the In the present paper, we investigate the existence of positive radial solutions of problem (1.1). There are several difficulties in facing this problem by means of variational methods.…”

Positive solutions for superdiffusive mixed problems

“…We refer to Bonanno, D'Agui & Papageorgiou [3], Filippucci, Pucci & Rȃdulescu [6], and Li, Ruf, Guo & Niu [9] for related results. We also refer to the monograph by Pucci & Serrin [11] for more results concerning the abstract setting of this paper.…”