Bidaut-Véron, Marie-Françoise Necessary conditions of existence for an elliptic equation with source term and measure data involving \(p\)-Laplacian. (English) Zbl 1114.35316 Electron. J. Differ. Equ. 2002, Conf. 08, 23-34 (2002). Summary: We study the nonnegative solutions to equation \[ -\Delta_p u=u^q+ \lambda\nu, \] in a bounded domain \(\Omega\) of \(\mathbb R^N\), where \(1< p< N\), \(q> p- 1\), \(\nu\) is a nonnegative Radon measure on \(\Omega\), and \(\lambda>0\) is a parameter. We give necessary conditions on \(\nu\) for existence, with \(\lambda\) small enough, in terms of capacity. We also give a priori estimates of the solutions. Cited in 11 Documents MSC: 35J60 Nonlinear elliptic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 35J25 Boundary value problems for second-order elliptic equations 35R05 PDEs with low regular coefficients and/or low regular data Keywords:degenerate quasilinear equations; measure data; capacities; a priori estimates PDFBibTeX XMLCite \textit{M.-F. Bidaut-Véron}, Electron. J. Differ. Equ. 2002, 23--34 (2002; Zbl 1114.35316) Full Text: EuDML EMIS