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Proceedings of the American Mathematical Society

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



Nonpositone elliptic problems in $ {\bf R}\sp n$

Authors: W. Allegretto and P. O. Odiobala
Journal: Proc. Amer. Math. Soc. 123 (1995), 533-541
MSC: Primary 35J65; Secondary 35B50
MathSciNet review: 1219715
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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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Keywords: Nonpositone, elliptic, positive decaying solution
Article copyright: © Copyright 1995 American Mathematical Society