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
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. https://doi.org/10.57262/die/1356060309
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