References
Dancer, E. N., On non-radially symmetric bifurcation, J. London Math. Soc., 20 (1979), 287–292.
Gidas, B., W. M. Ni & L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in ℝn, Comm. Math. Phys., 68 (1979), 209–243.
Palais, R., Seminar on the Atiyah-Singer Theorem, Annals of Math. Studies, No. 57, Princeton Univ. Press: Princeton 1965.
Smoller, J., & A. Tromba & A. Wasserman, Nondegenerate solutions of boundary-value problems, J. Nonlinear Anal., 4 (1980), 207–215.
Smoller, J., & A. Wasserman, Global bifurcation of steady-state solutions, J. Diff. Equations 39 (1981), 269–290.
Smoller, J., & A. Wasserman, Existence, uniqueness, and non-degeneracy of positive solutions of semilinear elliptic equations, Comm. Math. Phys., 95 (1984), 129–159.
Smoller, J., Shock Waves and Reaction-Diffusion Equations, Springer-Verlag: New York, 1983.
Vanderbauwhede, A., Local Bifurcation and Symmetry, Research Notes in Math., No. 75, Pitman: Boston, 1982.
Author information
Authors and Affiliations
Additional information
Communicated by J. Serrin
Rights and permissions
About this article
Cite this article
Smoller, J., Wasserman, A. Symmetry-breaking for positive solutions of semilinear elliptic equations. Arch. Rational Mech. Anal. 95, 217–225 (1986). https://doi.org/10.1007/BF00251359
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251359