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Gelfand type elliptic problems under Steklov boundary conditions
Authors:Elvise Berchio  Filippo GazzolaDario Pierotti
Institution:Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, 20133 Milano, Italy
Abstract:For a Gelfand type semilinear elliptic equation we extend some known results for the Dirichlet problem to the Steklov problem. This extension requires some new tools, such as non-optimal Hardy inequalities, and discovers some new phenomena, in particular a different behavior of the branch of solutions and three kinds of blow-up for large solutions in critical growth equations. We also show that small values of the boundary parameter play against strong growth of the nonlinear source.
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