Codice QDD 43 Titolo Gelfand type elliptic problems under Steklov boundary conditions Data 2009-04-17 Autore/i Berchio, E. ; Gazzola, F. ; Pierotti, D. Link Download full text 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.