DCDS
Multiple sign-changing solutions of an elliptic eigenvalue problem
Aixia Qian Shujie Li
Discrete & Continuous Dynamical Systems - A 2005, 12(4): 737-746 doi: 10.3934/dcds.2005.12.737
We prove the existences of multiple sign-changing solutions for a semilinear elliptic eigenvalue problem with constraint by using variational methods under weaker conditions.
keywords: Minimax theory sign-changing solution elliptic eigenvalue problems.
DCDS
Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity
Shujie Li Zhitao Zhang
Discrete & Continuous Dynamical Systems - A 1999, 5(3): 489-493 doi: 10.3934/dcds.1999.5.489
In this paper, we use Lyapunov-Schmidt method and Morse theory to study semilinear elliptic boundary value problems with resonance at infinity, and get new multiple solutions theorems.
keywords: Dirichlet problems resonance. multiple solutions
CPAA
On positive solutions of the elliptic sine-Gordon equation
Goong Chen Zhonghai Ding Shujie Li
Communications on Pure & Applied Analysis 2005, 4(2): 283-294 doi: 10.3934/cpaa.2005.4.283
The aim of this paper is to study positive solutions of the elliptic sine-Gordon equation on a bounded domain with homogeneous Dirichlet boundary condition, which models the steady state of the Josephson $\pi-$junction in superconductivity. The properties of positive solutions are investigated theoretically and numerically.
keywords: variational methods positive solutions. Elliptic sine-Gordon equation

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