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