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.
For more information see https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html
Reference15 articles.
1. J. M. Alonso, R. Ortega; Unbounded solutions of semilinear equations at resonance, Nonlinearity, 9 (1996) no. 5, 1099-1111.
2. B. Gidas, W.-M. Ni, L. Nirenberg; Symmetry and related properties via the maximum principle, Commun. Math. Phys., 68 (1979), 209-243.
3. S. P. Hastings, J. B. McLeod; Short proofs of results by Landesman, Lazer, and Leach on problems related to resonance, Di erential Integral Equations, 24 (2011) no. 5-6, 435-441.
4. P. Korman; Global Solution Curves for Semilinear Elliptic Equations, World Scienti c, Hackensack, NJ 2012.
5. P. Korman; Nonlinear elliptic equations and systems with linear part at resonance, Electron. J. Di erential Equations, 2016 (2016) No. 67.