Figueiredo, Giovany M. Multiplicity of solutions for a quasilinear problem with supercritical growth. (English) Zbl 1166.35301 Electron. J. Differ. Equ. 2006, Paper No. 31, 7 p. (2006). Summary: The multiplicity and concentration of positive solutions are established for the equation \[ -\varepsilon^{p}\Delta_{p}u+V(z)|u|^{p-2}u=|u|^{q-2}u +\lambda|u|^{s-2}u \quad\text{in }\mathbb{R}^N, \] where \(1<p<N\), \(\varepsilon >0\), \(p<q<p^* \leq s\), \(p^{*}=\frac{Np}{N-p}\), \(\lambda\geq 0\) and \(V\) is a positive continuous function. Cited in 3 Documents MSC: 35A15 Variational methods applied to PDEs 35H30 Quasielliptic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:Variational method; penalization method; Moser iteration method PDFBibTeX XMLCite \textit{G. M. Figueiredo}, Electron. J. Differ. Equ. 2006, Paper No. 31, 7 p. (2006; Zbl 1166.35301) Full Text: EuDML EMIS Link