Osaka Journal of Mathematics

Nonlinear elliptic equations with singular reaction

Nikolaos S. Papageorgiou and George Smyrlis

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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.

Article information

Osaka J. Math., Volume 53, Number 2 (2016), 489-514.

First available in Project Euclid: 27 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 35J67: Boundary values of solutions to elliptic equations


Papageorgiou, Nikolaos S.; Smyrlis, George. Nonlinear elliptic equations with singular reaction. Osaka J. Math. 53 (2016), no. 2, 489--514.

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