Article ID Journal Published Year Pages File Type
4613404 Journal of Differential Equations 2007 18 Pages PDF
Abstract

We study the existence of radial ground state solutions for the problem−div(∇u1+|∇u|2)=uq,u>0inRN,u(x)→0as|x|→∞,N⩾3N⩾3, q>1q>1. It is known that this problem has infinitely many ground states when q⩾N+2N−2, while no solutions exist if q⩽NN−2. A question raised by Ni and Serrin in [W.-M. Ni, J. Serrin, Existence and non-existence theorems for ground states for quasilinear partial differential equations, Atti Convegni Lincei 77 (1985) 231–257] is whether or not ground state solutions exist for NN−2

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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