Nonlinear elliptic equations with singular reaction
Nikolaos S. Papageorgiou, George Smyrlis · Osaka City University (Osaka City University) · 2016
We study a nonlinear elliptic equation with a singular term and a continuous perturbation. We look for positive solutions. We prove three multiplicity theorems producing at least two positive solutions. The first multiplicity theorem concerns equations driven by a nonhomogeneous in general differential operator. Also, two of the theorems have a superlinear perturbation (but without the Ambrosetti--Rabinowitz condition), while the third has a sublinear perturbation. Our approach is variational together with suitable truncation and comparison techniques.