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By Hugo Castro, Reviewed Alan and V. Lair

Abstract

Infinitely many nonradial solutions to a superlinear Dirichlet problem. (English summary) Proc. Amer. Math. Soc. 131 (2003), no. 3, 835–843 (electronic). The authors consider the equation ∆u + f(u) = 0 in the unit ball in R n, n ≥ 2, with homogeneous Dirichlet boundary condition. The function f ∈ C 1 (R) satisfies lim |t|→ ∞ f(t)/t = ∞ as well as several other conditions. The authors first prove a result showing that if the problem has a restricted number of radial solutions of a certain type, then it must have infinitely many nonradial solutions. They then use this result in order to prove that the problem has an infinite number of nonradial solutions if, for any a ∈ R and 1 < p < (n + 2)/n, f(u) = |u + a | p−1 (u + a)

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.363.3157
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