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Multiple single-peaked solutions of a class of semilinear Neumann problems via the category of the domain boundary

  • Nils Ackermann

Abstract.

For a smooth domain \(\Omega\) with compact boundary we investigate the problem \(-d^2\Delta u+u=f(u)\) with Neumann boundary conditions, where f has superlinear but subcritical growth. Provided that \(d>0\) is sufficiently small we show the existence of at least \(cat(\partial\Omega)\) positive solutions with single maximum points that lie on \(\partial\Omega\). We replace the standard variational setting used in the case of homogeneous f by considering the restriction of the free functional to a suitable submanifold of the Sobolev Space \(H^1(\Omega)\).

Keywords

Boundary Condition Sobolev Space Domain Boundary Neumann Boundary Maximum Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Nils Ackermann
    • 1
  1. 1. Mathematisches Institut, Justus Liebig Universität Gießen, Arndstr. 2, D-35392 Gießen, Germany (e-mail: Nils.Ackermann@math.uni-giessen.de) DE

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