On the elliptic equation $\Delta u=\varphi (x)u^ \gamma$ in $\textbf {R}^ 2$
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- by Nichiro Kawano, TakaΕi Kusano and Manabu Naito PDF
- Proc. Amer. Math. Soc. 93 (1985), 73-78 Request permission
Abstract:
The equation $( * )\Delta u = \phi (x){u^\gamma }$ is considered in ${{\mathbf {R}}^2}$, where $\gamma \ne 1$ and $\phi (x) \geqslant 0$ is locally HΓΆlder continuous. Sufficient conditions are obtained for $( * )$ to possess infinitely many positive solutions which are defined throughout ${R^2}$ and have logarithmic growth as $|x| \to \infty$. An extension of the main result to the higher-dimensional case is also attempted.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 73-78
- MSC: Primary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-1985-0766530-X
- MathSciNet review: 766530