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.

Gelfand type elliptic problems under Steklov boundary conditions / Berchio, Elvise; Gazzola, F.; D., Pierotti. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 27:(2010), pp. 315-335. [10.1016/j.anihpc.2009.09.011]

Gelfand type elliptic problems under Steklov boundary conditions

BERCHIO, ELVISE;
2010

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2522499
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