Herrero García, Miguel Ángel and Velázquez, J.J. L. (1991) Radial solutions of a semilinear elliptic problem. Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 118 (3-4). pp. 305-326. ISSN 0308-2105
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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 element-of 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/1-p) or if f(r) ≈ cr2p/1-p as r --> ∞, where [GRAPHICS] When f(r) = c*r2p/1-p + h(r) with h(r) = o(r2p/1-p) 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 --> ∞.
|Uncontrolled Keywords:||Equation; RN; set of nonnegative; global and radial solutions|
|Subjects:||Sciences > Mathematics > Differential equations|
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|Deposited On:||20 Nov 2012 13:41|
|Last Modified:||20 Nov 2012 13:41|
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