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Multiple solutions of semilinear elliptic equations in exterior domains

Published online by Cambridge University Press:  14 July 2008

Huei-Li Lin
Center for General Education, Chang Gung University, Kwei-San, Tao-Yuan 333, Taiwan, ROC (


In this paper, assume that $q$ is a positive continuous function in $\mathbb{R}^{N}$ satisfying suitable conditions. We prove that the Dirichlet problem $-\Delta u+u=q(z)|u|^{p-2}u$ in an exterior domain admits at least two positive solutions and a solution which changes sign.

Research Article
2008 Royal Society of Edinburgh

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