MR2197533 Franca, Matteo Matteo FRANCA Ground States and Singular Ground States for Quasilinear Elliptic Equation in the Subcritical Case Funkcialaj Ekvacioj. Serio Internacia 48 2005 331--349 http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-3/48_331.pdf http://www.ams.org/mathscinet-getitem?mr=MR2197533 We consider radial solution $u(|x|)$, $x\in R^n$, of a $p$-Laplace equation with non-linear potential depending also on the space variable $x$. We assume that the potential is polynomial and it is negative for $u$ small and positive and subcritical for $u$ large.<br />     We prove the existence of radial Ground States under suitable Hypotheses on the potential $f(u,|x|)$. Furthermore we prove the existence of uncountably many radial Singular Ground States; this last result seems to be new even for the spatial independent case and even for $p=2$.<br />     The proofs combine an energy analysis and the dynamical systems approach developed by Johnson, Pan, Yi and Battelli for the $p=2$ case. $p$-Laplace equations, Radial solution, Regular/Singular ground state, Fowler inversion, Invariant manifold. 35J70, 35J10, 37D10. 48-331 2005 Ground States and Singular Ground States for Quasilinear Elliptic Equation in the Subcritical Case FRANCA, Matteo Matteo FRANCA
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