Parametric and nonparametric A -Laplace problems: Existence of solutions and asymptotic analysis

Abstract

We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain Ω. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to $0^{+}$ . In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators.

Keywords

Dirichlet boundary value problem asymptotic analysis Orlicz–Sobolev space

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