Positive solution for nonlinear elliptic equations on symmetric domains. (English) Zbl 07906584
Summary: We show the existence of a positive solution for the Schrödinger quasilinear equation with variable exponents above the critical regime. For that matter, we show an embedding into an Orlicz space of functions modeled over radially symmetric domains. Then we use a Galerkin method combined with a fixed-point argument to obtain a solution.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35B09 | Positive solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
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