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Semilinear elliptic problems with nonlinear boundary conditions. (English) Zbl 0985.35032

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.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J20 Variational methods for second-order elliptic equations
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