Chipot, Michel; Ramaswamy, Mythily Semilinear elliptic problems with nonlinear boundary conditions. (English) Zbl 0985.35032 Differ. Equ. Dyn. Syst. 6, No. 1-2, 51-75 (1998). Summary: A semilinear elliptic problem with mixed boundary conditions, nonlinear Neumann on one part and homogeneous Dirichlet on the rest of the boundary is considered in a bounded domain \(\Omega\subset \mathbb{R}^N\), \(N\geq 2\). Depending on the interaction of the two nonlinearities, a nonexistence theorem and some existence theorems for positive solutions are obtained using variational methods. Cited in 1 Document MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35J20 Variational methods for second-order elliptic equations Keywords:nonlinear Neumann condition; Dirichlet conditions; nonexistence; existence; variational methods PDFBibTeX XMLCite \textit{M. Chipot} and \textit{M. Ramaswamy}, Differ. Equ. Dyn. Syst. 6, No. 1--2, 51--75 (1998; Zbl 0985.35032)