Positive solutions for a quasilinear degenerate elliptic equation in \(\mathbb R^ N\)
The existence of a positive, spherically symmetric solution on \(\mathbb R^ N\), which vanishes as \(| x| \to +\infty\), of the degenerate elliptic equation \(D(| Du|^{p-2} Du)+f(u)=0\) is studied. The method used in the proof of the existence of such a solution is the constrained minimization method as by \textit{H. Berestycki} and \textit{P. L. Lions} [Arch. Ration. Mech. Anal. 82, 313--345 (1983; Zbl 0533.35029)] for the linear case \((p=2)\).
scientific article; zbMATH DE number 4077833
scientific article