Electron. J. Differential Equations, Vol. 2024 (2024), No. 09, pp. 1-8.

Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two

Philip Korman

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.
DOI: 10.58997/ejde.2024.09

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Philip Korman
Department of Mathematical Sciences
University of Cincinnati
Cincinnati OH 45221-0025, USA
email: kormanp@ucmail.edu

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