Parametric and nonparametric A -Laplace problems: Existence of solutions and asymptotic analysis
Calogero Vetro · Asymptotic Analysis · 2020
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 [Formula: see text]. 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.