Open Access
6 November 2003 Existence and nonexistence of entire solutions to the logistic differential equation
Marius Ghergu, Vicenţiu Rădulescu
Abstr. Appl. Anal. 2003(17): 995-1003 (6 November 2003). DOI: 10.1155/S1085337503305020


We consider the one-dimensional logistic problem (rαA(|u|)u)=rαp(r)f(u) on (0,), u(0)>0, u(0)=0, where α is a positive constant and A is a continuous function such that the mapping tA(|t|) is increasing on (0,). The framework includes the case where f and p are continuous and positive on (0,), f(0)=0, and f is nondecreasing. Our first purpose is to establish a general nonexistence result for this problem. Then we consider the case of solutions that blow up at infinity and we prove several existence and nonexistence results depending on the growth of p and A. As a consequence, we deduce that the mean curvature inequality problem on the whole space does not have nonnegative solutions, excepting the trivial one.


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Marius Ghergu. Vicenţiu Rădulescu. "Existence and nonexistence of entire solutions to the logistic differential equation." Abstr. Appl. Anal. 2003 (17) 995 - 1003, 6 November 2003.


Published: 6 November 2003
First available in Project Euclid: 10 November 2003

zbMATH: 1111.34004
MathSciNet: MR2029521
Digital Object Identifier: 10.1155/S1085337503305020

Primary: 26D10 , 34A34
Secondary: 34B18 , 34D05 , 35B40

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 17 • 6 November 2003
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