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Herrero, Miguel A. and Velázquez, J.J. L. (1991) Radial solutions of a semilinear elliptic problem. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 118 (34). pp. 305326. ISSN 03082105

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Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8244935
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Abstract
We analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equation Δu + u(p) = f in R(N), N ≥ 1, where 0 < p < 1, and f elementof L(loc)1(R(N)) is a radial and almost everywhere nonnegative function. We show that radial solutions of (E) exist if f(r) = o(r2p/1p) or if f(r) ≈ cr2p/1p as r > ∞, where [GRAPHICS] When f(r) = c*r2p/1p + h(r) with h(r) = o(r2p/1p) as r > ∞, radial solutions continue to exist if h(r) is sufficiently small at infinity. Existence, however, breaks down if h(r) > 0, [GRAPHICS] Whenever they exist, radial solutions are characterised in terms of their asymptotic behaviour as r > ∞.
Item Type:  Article 

Uncontrolled Keywords:  Equation; RN; set of nonnegative; global and radial solutions 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  17132 
Deposited On:  20 Nov 2012 12:41 
Last Modified:  12 Dec 2018 15:08 
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