The supercritical Lane-Emden-Fowler equation in exterior domains
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Date
2007
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TAYLOR & FRANCIS INC
Abstract
We consider the exterior problem
Delta u + u(p) = 0, u > 0 in IRN\(D) over bar,
u = 0 on partial derivative D, lim(vertical bar x vertical bar ->+infinity) u(x) = 0
where D is a bounded, smooth domain in IRN, for supercritical powers p > 1. We prove that if N > 4 and p > N-3/N-3, then this problem admits infinitely many solutions. If D is symmetric with respect to N axes, this result holds whenever N >= 3 and p > N+2/N-2.
Delta u + u(p) = 0, u > 0 in IRN\(D) over bar,
u = 0 on partial derivative D, lim(vertical bar x vertical bar ->+infinity) u(x) = 0
where D is a bounded, smooth domain in IRN, for supercritical powers p > 1. We prove that if N > 4 and p > N-3/N-3, then this problem admits infinitely many solutions. If D is symmetric with respect to N axes, this result holds whenever N >= 3 and p > N+2/N-2.
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Keywords
critical exponents, linearized operators, slow decay solutions, POSITIVE SOLUTIONS, ELLIPTIC-EQUATIONS, DIRICHLET PROBLEMS, BOUNDED DOMAINS, DELTA-U, EXISTENCE, CONVERGENCE