(N,q)‐Laplacian equations with one‐sided critical exponential growth
Abstract
Abstract We prove the existence of two non‐trivial weak solutions for a class of quasilinear, non‐homogeneous elliptic problems driven by the ‐Laplacian with one‐sided critical exponential growth in a bounded domain . The first solution is obtained as a local minimizer of the associated energy functional; to justify this, we establish that any local minimum in the topology is also a local minimum in the natural topology. This minimization result is proved in a more general setting and may be useful in related problems. The second solution is given by minimax methods.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Optimization and Variational Analysis
Publication details
- Journal / source
- Mathematische Nachrichten
- Volume
- 299
- Issue
- 3
- Pages
- 675–698
- Publication date
- 16 February 2026
- Language
- EN