Titolo: Nodal solutions to critical growth elliptic problems under Steklov boundary conditions
Periodico: Università degli Studi del Piemonte Orientale 'A. Avogadro' : Facoltà di Economia - Dipartimento di Scienze Economiche e Metodi Quantitativi "SEMEQ" - Quaderni
Anno: 2008 - Fascicolo: 1 - Pagina iniziale: 1 - Pagina finale: 26

We study elliptic problems at critical growth under Steklov boundary conditions in bounded domains. For a second order problem we prove existence of nontrivial nodal solutions. These are obtained by combining a suitable linking argument with ¯ne estimates on the concentration of Sobolev minimizers on the boundary. When the domain is the unit ball, we obtain a multiplicity result by taking advantage of the explicit form of the Steklov eigenfunctions. We also partially extend the results in the ball to the case of fourth order Steklov boundary value problems.




Testo completo: http://semeq.unipmn.it/files/quaderno%2001.08.pdf

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