Solutions of nonlinear planar elliptic problems with triangle symmetry



- Stanislaus Maier-Paape, Thomas Wanner:
Solutions of nonlinear planar elliptic problems with triangle symmetry
Journal of Differential Equations 136(1), pp. 1-34, 1997.
Abstract
In this paper we continue the study of the nodal domain structure of doubly periodic solutions of certain nonlinear elliptic problems initiated in Fife, Kielhöfer, Maier-Paape, Wanner (1997). More precisely, we consider small amplitude solutions of in whose nodal domains consist of equilateral triangles tiling the plane. If this equation is suitably perturbed, then for generic we prove the existence of unique nearby solutions with triangle symmetry and show how their nodal domain geometry breaks up. Furthermore, we treat the non-generic rectangular cases which had to be excluded in Fife, Kielhöfer, Maier-Paape, Wanner (1997), as well as other nodal domain structures.
Links
The published version of the paper can be found at https://doi.org/10.1006/jdeq.1996.3240.
Bibtex
@article{maier:wanner:97a,
author = {Stanislaus Maier-Paape and Thomas Wanner},
title = {Solutions of nonlinear planar elliptic problems with
triangle symmetry},
journal = {Journal of Differential Equations},
year = 1997,
volume = 136,
number = 1,
pages = {1--34},
doi = {10.1006/jdeq.1996.3240}
}