do Ó, João Marcos; Medeiros, Everaldo S. Remarks on least energy solutions for quasilinear elliptic problems in \(\mathbb R^N\). (English) Zbl 1109.35318 Electron. J. Differ. Equ. 2003, Paper No. 83, 14 p. (2003). The authors consider the quasilinear elliptic problem \[ -\Delta_p w= g(w),\quad\text{ in }\mathbb R^N,\tag{1} \] where \(\Delta_p u= \text{div}(|\nabla u|^{p-2}\nabla u)\) is the \(p\)-Laplacian operator and \(1< p\leq N\). Using variational methods more precisely by a constrained minimization argument, they show the existence of ground states solutions (or least energy solutions) for the (1) in both cases, \(1< p< N\) and \(p= N\). They prove also that the mountain-pass value gives the least energy level and obtain the exponential decay of the derivatives of the solutions of (1). Reviewer: Messoud A. Efendiev (Berlin) Cited in 13 Documents MSC: 35J20 Variational methods for second-order elliptic equations 35J60 Nonlinear elliptic equations Keywords:Variational methods; minimax methods; superlinear elliptic problems; \(p\)-Laplacian; ground-states; mountain-pass solutions PDFBibTeX XMLCite \textit{J. M. do Ó} and \textit{E. S. Medeiros}, Electron. J. Differ. Equ. 2003, Paper No. 83, 14 p. (2003; Zbl 1109.35318) Full Text: EuDML EMIS