Gelfand type elliptic problems under Steklov boundary conditions |
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Authors: | Elvise Berchio Filippo GazzolaDario Pierotti |
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Institution: | Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, 20133 Milano, Italy |
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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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