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1995 A priori estimates and uniqueness of inflection points for positive solutions of semipositone problems
Joseph A. Iaia
Differential Integral Equations 8(2): 393-403 (1995).

Abstract

We prove that positive solutions of $-\Delta u = \lambda f(u)$ in $\Omega$ and $u = 0$ on $\partial \Omega$ where $f$ is increasing, concave, and $f(0) < 0$ satisfy $c_{1} \leq {\lambda f(d) \over d} \leq c_{2}$ where $d = \sup u.$ Also, we show that solutions of the above have exactly one inflection point.

Citation

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Joseph A. Iaia. "A priori estimates and uniqueness of inflection points for positive solutions of semipositone problems." Differential Integral Equations 8 (2) 393 - 403, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0816.34028
MathSciNet: MR1296131

Subjects:
Primary: 35J65
Secondary: 34B15, 35B05

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 2 • 1995
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