Necessary and sufficient condition for existence at resonance for eigenvalues of multiplicity two
arXiv:2601.06623
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.
10 pages, 1 figure, comments are welcome