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2004 Stable solutions on $\R^n$ and the primary branch of some non-self-adjoint convex problems
E. N. Dancer
Differential Integral Equations 17(9-10): 961-970 (2004).

Abstract

We prove that if $n = 2$ or $3$, the problem $- \Delta u = e^u$ on $R^n$ has no stable negative solution. We then use this to remove self-adjointness conditions in a paper of Crandall and Rabinowitz on the primary branch of positive solutions of a nonlinear boundary-value problem.

Citation

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E. N. Dancer. "Stable solutions on $\R^n$ and the primary branch of some non-self-adjoint convex problems." Differential Integral Equations 17 (9-10) 961 - 970, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.35357
MathSciNet: MR2082455

Subjects:
Primary: 35J60
Secondary: 47J05

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 9-10 • 2004
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