Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 09, pp. 1-8.

Title: Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two
       
Author: Philip Korman (Univ. of Cincinnati, Cincinnati OH, USA)

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.

Submitted December 22, 2023. Published January 24, 2024.
Math Subject Classifications: 35J25.
Key Words: Existence of solutions; Landesman-Lazer condition; resonance.