Gelfand type elliptic problems under Steklov boundary conditions

Berchio, Elvise; Gazzola, Filippo; Pierotti, Dario

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 315-335.

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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