Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces
Abstract
ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type where is a parameter, is a bounded domain in () with smooth boundary . The first class we drop the ‐condition of the functions () and assume that has a double criticality. For this class, we use a linking theorem without the Palais‐Smale condition for locally Lipschitz functionals combined with a concentration‐compactness lemma for nonreflexive Orlicz–Sobolev space. The second class, we relax the ‐condition of the functions (). For this class, we consider and and obtain the proof based on a saddle‐point theorem of Rabinowitz without the Palais‐Smale condition for functionals Fréchet differentiable combined with some properties of the weak topology.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Volume
- 49
- Issue
- 12
- Pages
- 13324–13360
- Publication date
- 14 April 2026
- Language
- EN