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Positive solutions for nonparametric anisotropic singular solutions

Papageorgiou Nikolaos S., Rădulescu Vicenţiu D., Sun Xueying

Opuscula Mathematica

2024

Vol. 44, no. 3

409--423

We consider an elliptic equation driven by a nonlinear, nonhomogeneous differential operator with nonstandard growth. The reaction has the combined effects of a singular term and of a “superlinear” perturbation. There is no parameter in the problem. Using variational tools and truncation and comparison techniques, we show the existence of at least two positive smooth solutions.