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Nonlinear Helmholtz equations with sign-changing diffusion coefficient
- Source :
- Comptes Rendus. Mathématique, 360 (G5), 513–538
- Publication Year :
- 2022
- Publisher :
- Cellule MathDoc/CEDRAM, 2022.
-
Abstract
- In this paper, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak -coercivity theory. All eigenvalues are proved to be bifurcation points and the bifurcating branches are investigated both theoretically and numerically. In a one-dimensional model example we obtain the existence of infinitely many bifurcating branches that are mutually disjoint, unbounded, and consist of solutions with a fixed nodal pattern.
Details
- ISSN :
- 17783569
- Volume :
- 360
- Database :
- OpenAIRE
- Journal :
- Comptes Rendus. Mathématique
- Accession number :
- edsair.doi.dedup.....f7f2f35de7925c249ffdfa694494df0e