We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which exhibits the competing effects of a parametric singular term and of a superlinear perturbation. Using variational methods together with truncation and comparison techniques, we show that for all small values of the parameter, the problem has at least two positive smooth solutions.
Papageorgiou, N.S., Vetro, C., Vetro, F. (2026). Nonlinear singular problems with an indefinite perturbation. REVISTA MATEMÁTICA COMPLUTENSE, 39, 117-133 [10.1007/s13163-025-00529-5].
Nonlinear singular problems with an indefinite perturbation
Vetro C.
;Vetro F.
2026-07-23
Abstract
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which exhibits the competing effects of a parametric singular term and of a superlinear perturbation. Using variational methods together with truncation and comparison techniques, we show that for all small values of the parameter, the problem has at least two positive smooth solutions.
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