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Nonlinear Helmholtz equations with sign-changing diffusion coefficient
Rainer Mandel1 ; Zoïs Moitier1 ; Barbara Verfürth2
1 Karlsruhe Institute of Technology, Institute for Analysis, Englerstraße 2, D-76131 Karlsruhe, Germany.
2 Karlsruhe Institute of Technology, Institute for Applied and Numerical Mathematics Englerstraße 2, D-76131 Karlsruhe, Germany.
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 513-538.

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 T-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.

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DOI : 10.5802/crmath.322
Classification : 35B32, 47A10

Rainer Mandel 1 ; Zoïs Moitier 1 ; Barbara Verfürth 2

1 Karlsruhe Institute of Technology, Institute for Analysis, Englerstraße 2, D-76131 Karlsruhe, Germany.
2 Karlsruhe Institute of Technology, Institute for Applied and Numerical Mathematics Englerstraße 2, D-76131 Karlsruhe, Germany.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Rainer Mandel; Zoïs Moitier; Barbara Verfürth. Nonlinear Helmholtz equations with sign-changing diffusion coefficient. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 513-538. doi : 10.5802/crmath.322. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.322/

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