Volume 10, Number 3, Fall 2002
An ODE Approach for ΔU + λU^{p}  U^{γ}= 0 in R^{N}; γ∈(0, 1), P > 0
TADIE
Abstract. The equation Δu + λu^{p}  u^{γ}= 0 governs
various phenomena in physics. When the domain in which the
Dirichlet problem is posed is a ball and the second member is an
increasing function of u, the solutions are radially symmetric.
That is why we consider a corresponding ODE problem. For
crossing solutions, unlike the cases we have come accross in the
literature [1], [7], we consider p ∈ (0, (n + 2)/(n  2)). We
obtain unique solutions in C^{1}(B_{R}) (not only in C^{2}(B_{R})).
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