Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the elliptic equation $\Delta u=\varphi (x)u^ \gamma$ in $\textbf {R}^ 2$
HTML articles powered by AMS MathViewer

by Nichiro Kawano, Takaŝi 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
  • R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. MR 0221256
  • Nichiro Kawano, On bounded entire solutions of semilinear elliptic equations, Hiroshima Math. J. 14 (1984), no.Β 1, 125–158. MR 750393
  • Wei Ming Ni, On the elliptic equation $\Delta u+K(x)u^{(n+2)/(n-2)}=0$, its generalizations, and applications in geometry, Indiana Univ. Math. J. 31 (1982), no.Β 4, 493–529. MR 662915, DOI 10.1512/iumj.1982.31.31040
  • Wei Ming Ni, On the elliptic equation $\Delta u+K(x)e^{2u}=0$ and conformal metrics with prescribed Gaussian curvatures, Invent. Math. 66 (1982), no.Β 2, 343–352. MR 656628, DOI 10.1007/BF01389399
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35J60
  • Retrieve articles in all journals with MSC: 35J60
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