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.
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@article{CRMATH_2022__360_G5_513_0,
author = {Mandel, Rainer and Moitier, Zo{\"\i}s and Verf\"urth, Barbara},
title = {Nonlinear {Helmholtz} equations with sign-changing diffusion coefficient},
journal = {Comptes Rendus. Math\'ematique},
pages = {513--538},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
number = {G5},
year = {2022},
doi = {10.5802/crmath.322},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/crmath.322/}
}
TY - JOUR AU - Mandel, Rainer AU - Moitier, Zoïs AU - Verfürth, Barbara TI - Nonlinear Helmholtz equations with sign-changing diffusion coefficient JO - Comptes Rendus. Mathématique PY - 2022 SP - 513 EP - 538 VL - 360 IS - G5 PB - Académie des sciences, Paris UR - http://archive.numdam.org/articles/10.5802/crmath.322/ DO - 10.5802/crmath.322 LA - en ID - CRMATH_2022__360_G5_513_0 ER -
%0 Journal Article %A Mandel, Rainer %A Moitier, Zoïs %A Verfürth, Barbara %T Nonlinear Helmholtz equations with sign-changing diffusion coefficient %J Comptes Rendus. Mathématique %D 2022 %P 513-538 %V 360 %N G5 %I Académie des sciences, Paris %U http://archive.numdam.org/articles/10.5802/crmath.322/ %R 10.5802/crmath.322 %G en %F CRMATH_2022__360_G5_513_0
Mandel, Rainer; Moitier, Zoïs; Verfürth, Barbara. Nonlinear Helmholtz equations with sign-changing diffusion coefficient. Comptes Rendus. Mathématique, Tome 360 (2022) no. G5, pp. 513-538. doi : 10.5802/crmath.322. http://archive.numdam.org/articles/10.5802/crmath.322/
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