Nontrivial solutions for some semilinear problems and applications to wave equations on ball and on sphere
(1995) Topological Methods in Nonlinear Analysis — Vol. 5, p. 177-192 (1995)
Files
1479287026.pdf
Closed Access - Adobe PDF
- 226.07 KB
Details
- Authors
- Abstract
- This paper is devoted to some multiplicity results for nontrivial solutions of nonlinear wave equations on balls and on spheres. These results follow from an abstract theorem which is obtained via a continuation theorem due to Berkovits and Mustonen [5] based on degree theoretic arguments. The framework to which the abstract theorem will be applied is the following. We consider the equation Au = N(u) in L 2 (M), where M is a measure space, A is a densely defined closed linear operator with closed range and N is the Nemytski˘ı operator generated by a Carath´eodory function (x, s) → g(x, s) from M × R to R. Our basic result is obtained for the above equation when, as in [4], one simple eigenvalue of A is crossed by the function h(x, s) := s −1 g(x, s) as s goes from −∞ to ∞. But in contrast to [4], here A is not assumed to be self-adjoint.
- Affiliations
Citations
Ben-Naoum, A. K., & Berkovits, J. (1995). Nontrivial solutions for some semilinear problems and applications to wave equations on ball and on sphere. Topological Methods in Nonlinear Analysis, 5, 177-192. https://hdl.handle.net/2078.5/177782 (Original work published 1995)