Necessary and sufficient condition for existence at resonance for eigenvalues of multiplicity two
Abstract
We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Differential Equations and Boundary Problems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 January 2026
- Document type
- Preprint