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

Article type: Research Article

Authors: Vetro, Calogero^{; *}

Affiliations: University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123 – Palermo, Italy. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

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, A-Laplace operator, asymptotic analysis, Orlicz–Sobolev space

DOI: 10.3233/ASY-201612

Journal: Asymptotic Analysis, vol. 122, no. 1-2, pp. 105-118, 2021