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Positive Solutions of Semilinear Differential Equations with Singularities

K. Lan,J. Webb

Published 1998 in Journal of Differential Equations

ABSTRACT

for example, see [3, 7, 8, 18, and 23]. Moreover, Eq. (1.1) contains many important equations which arise from other fields. For example, the generalized Emden Fowler equation, where f =z , p>0 and g is continuous (see [21] and [24]), arises in the fields of gas dynamics, nuclear physics, and chemically reacting systems [24]; and the Thomas Fermi equation, where f =z 2 and g=t , so g has a singularity at 0 (see [9, 10 and 21]), was developed in studies of atomic structures (see, for example, [21]) and atomic calculations [5]. When g is continuous, the existence of positive solutions of Eq. (1.1) with suitable boundary conditions has been studied in [23] by using normtype cone expansion and compression theorems. The key conditions on f are either f is superlinear, that is, limx 0 f (x) x=0 and limx f (x) x= or f is sublinear, that is, limx 0 f (x) x= and limx 0 f (x) x=0. However, it is known that Eq. (1.1) with g#1 has positive solutions for article no. DE983475

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