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Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions. (English) Zbl 0733.35038
From the authors’ introduction: “In this paper we shall study non- constant radially symmetric solutions of the problem \[ (I)\quad -\Delta u=\lambda (u^ p-u^ q)\text{ in } B,\quad u>0\text{ in } B,\quad \partial u/\partial n=0\text{ on } \partial B, \] where B is the unit ball in \({\mathbb{R}}^ N\) \((N>2)\) and n is the outward pointing normal, \(p=(N+2)/(N-2)\), \(0<q<p-1=4/(N-2)\). In addition we shall only consider those solutions of Problem (I) which are decreasing in \(r=| x|\).”
Reviewer: M.Chicco (Genova)

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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