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2009, Volume 8, Issue 2: 533-557. Doi: 10.3934/cpaa.2009.8.533
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Nodal solutions to critical growth elliptic problems under Steklov boundary conditions

  • 1.

    Dipartimento SEMEQ, Università del Piemonte Orientale, via E. Perrone 18, Novara, 28100

  • 2.

    Dipartimento di Matematica Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano

  • 3.

    Dipartimento di Matematica del Politecnico, Piazza L. da Vinci 32, Milano, 20133

Received:  January 2008
Revised:  July 2008
Published:  March 2009
Abstract / Introduction Related Papers Cited by
    Abstract
  • 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 fine 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.
    Mathematics Subject Classification: Primary: 35J20, 35J35; Secondary: 35J40.

    Citation:
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