# American Institute of Mathematical Sciences

2005, 2005(Special): 886-894. doi: 10.3934/proc.2005.2005.886

## Stability and symmetry breaking of solutions of semilinear elliptic equations

 1 Department of Applied Mathematics, Hsuan Chuang University, Hsinchu, Taiwan

Received  July 2004 Revised  March 2005 Published  September 2005

In this article, we prove that there are three unstable positive solutions of a semilinear elliptic equation in a two bumps domain or in a one hole domain in which one is axially symmetric and the other two are nonaxially symmetric.
Citation: Hwai-Chiuan Wang. Stability and symmetry breaking of solutions of semilinear elliptic equations. Conference Publications, 2005, 2005 (Special) : 886-894. doi: 10.3934/proc.2005.2005.886
 [1] Daoyin He, Ingo Witt, Huicheng Yin. On the strauss index of semilinear tricomi equation. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4817-4838. doi: 10.3934/cpaa.2020213 [2] Antonio Azzollini. On a functional satisfying a weak Palais-Smale condition. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 1829-1840. doi: 10.3934/dcds.2014.34.1829 [3] Scott Nollet, Frederico Xavier. Global inversion via the Palais-Smale condition. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 17-28. doi: 10.3934/dcds.2002.8.17 [4] A. Azzollini. Erratum to: "On a functional satisfying a weak Palais-Smale condition". Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4987-4987. doi: 10.3934/dcds.2014.34.4987 [5] Rafael Ortega. Stability and index of periodic solutions of a nonlinear telegraph equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 823-837. doi: 10.3934/cpaa.2005.4.823 [6] Kazuhiro Ishige, Michinori Ishiwata. Global solutions for a semilinear heat equation in the exterior domain of a compact set. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 847-865. doi: 10.3934/dcds.2012.32.847 [7] Lucio Cadeddu, Giovanni Porru. Symmetry breaking in problems involving semilinear equations. Conference Publications, 2011, 2011 (Special) : 219-228. doi: 10.3934/proc.2011.2011.219 [8] Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083 [9] Xin Liu. Compressible viscous flows in a symmetric domain with complete slip boundary: The nonlinear stability of uniformly rotating states with small angular velocities. Communications on Pure & Applied Analysis, 2019, 18 (2) : 751-794. doi: 10.3934/cpaa.2019037 [10] Shoichi Hasegawa. Stability and separation property of radial solutions to semilinear elliptic equations. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 4127-4136. doi: 10.3934/dcds.2019166 [11] Mamadou Sango. Homogenization of the Neumann problem for a quasilinear elliptic equation in a perforated domain. Networks & Heterogeneous Media, 2010, 5 (2) : 361-384. doi: 10.3934/nhm.2010.5.361 [12] Francesco Della Pietra, Ireneo Peral. Breaking of resonance for elliptic problems with strong degeneration at infinity. Communications on Pure & Applied Analysis, 2011, 10 (2) : 593-612. doi: 10.3934/cpaa.2011.10.593 [13] Muhammad Usman, Bing-Yu Zhang. Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1509-1523. doi: 10.3934/dcds.2010.26.1509 [14] Joseph A. Iaia. Localized radial solutions to a semilinear elliptic equation in $\mathbb{R}^n$. Conference Publications, 1998, 1998 (Special) : 314-326. doi: 10.3934/proc.1998.1998.314 [15] Ruofei Yao, Yi Li, Hongbin Chen. Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus. Discrete & Continuous Dynamical Systems, 2019, 39 (3) : 1585-1594. doi: 10.3934/dcds.2018122 [16] Yinbin Deng, Shuangjie Peng, Li Wang. Existence of multiple solutions for a nonhomogeneous semilinear elliptic equation involving critical exponent. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 795-826. doi: 10.3934/dcds.2012.32.795 [17] Constantin Christof, Christian Meyer, Stephan Walther, Christian Clason. Optimal control of a non-smooth semilinear elliptic equation. Mathematical Control & Related Fields, 2018, 8 (1) : 247-276. doi: 10.3934/mcrf.2018011 [18] Christos Sourdis. A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart. Electronic Research Archive, , () : -. doi: 10.3934/era.2021016 [19] Zongming Guo, Yunting Yu. Boundary value problems for a semilinear elliptic equation with singular nonlinearity. Communications on Pure & Applied Analysis, 2016, 15 (2) : 399-412. doi: 10.3934/cpaa.2016.15.399 [20] Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243

Impact Factor: