Existence and nonexistence of entire solutions to the logistic differential equation

Marius Ghergu and Vicenţiu Rădulescu

Abstract and Applied Analysis, 2003, vol. 2003, issue 17, 995-1003

Abstract: 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.

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/S1085337503305020

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:17:p:995-1003

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().