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Volume 10,     Number 3,     Fall 2002


An ODE Approach for ΔU + λUp - U= 0 in RN; γ∈(0, 1), P > 0

Abstract. The equation Δu + λup - u= 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 C1(BR) (not only in C2(BR)).


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