Nonpositone elliptic problems in $\textbf {R}^ n$
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- by W. Allegretto and P. O. Odiobala
- Proc. Amer. Math. Soc. 123 (1995), 533-541
- DOI: https://doi.org/10.1090/S0002-9939-1995-1219715-9
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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 $l = - \Delta$.References
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Bibliographic 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