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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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Nonpositone elliptic problems in $\textbf {R}^ n$
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by W. Allegretto and P. O. Odiobala PDF
Proc. Amer. Math. Soc. 123 (1995), 533-541 Request permission

Abstract:

We consider the problem of the existence of positive decaying solutions in ${\mathbb {R}^n}$ to the nonlinear equation $lu = \lambda f(x,u)$ where l denotes a second-order uniformly elliptic operator and $f(x,u)$ is superlinear and subcritical with $f(x,0) \leq 0$. Existence is obtained by Mountain Pass Arguments and positivity by establishing bounds for u in various Sobolev norms and by comparison with the case $l = - \Delta$.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 533-541
  • MSC: Primary 35J65; Secondary 35B50
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1219715-9
  • MathSciNet review: 1219715