Neumann problems driven by competing and non-competing operators
Abstract
This paper studies quasi-linear equations driven by competing and non-competing operators subject to the Neumann boundary condition. In the case of competing operators, the existence of a generalized or strong generalized solution is proven. This is the first time such results are obtained for the Neumann boundary condition. In the case of non-competing operators, the existence of a weak solution is proven using the same type of reasoning based on finite-dimensional approximation. A unifying treatment in both cases is developed.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Contact Mechanics and Variational Inequalities
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 24
- Issue
- 0
- Pages
- 168–178
- Publication date
- 1 January 2026