IJPAM: Volume 73, No. 2 (2011)

SOME SPECIAL SOLUTIONS OF $u'' = h(r,u)$, $r>0$:

Mathematics Institut
5, Universitetsparken
Copenhagen, 2100, DENMARK
[email protected]

Abstract. The type of equations displayed above is often used for the modelling of various physical, chemical and biological phenomena and they have been subject to lots of investigations lately. Beside their importance as solutions of an ODE, the solutions of those equation can provide some lights on the properties of the solutions of some multidimensional elliptic equations. We are looking for decreasing solutions which have compact supports and increasing ones in some $[0,R)$ which have dead-core space. We find out that these various solutions can be obtained just by giving various data to the initial or boundary conditions. For the hypotheses, we require $h$ to be continuous, nonegative and strictly positive whenever the last argument is zero and to be increasing in the second argument.

Received: July 28, 2011

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 2