Necessary and sufficient condition for existence at resonance for eigenvalues of multiplicity two
Analysis of PDEs
2026-01-13 v1 Classical Analysis and ODEs
Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2601.06623,
title = {Necessary and sufficient condition for existence at resonance for eigenvalues of multiplicity two},
author = {Philip Korman},
journal= {arXiv preprint arXiv:2601.06623},
year = {2026}
}
Comments
10 pages, 1 figure, comments are welcome