Abstract
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.
Citation
Nikolaos S. Papageorgiou. George Smyrlis. "Nonlinear elliptic equations with singular reaction." Osaka J. Math. 53 (2) 489 - 514, April 2016.
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