Nodal solutions to superlinear biharmonic equations via decomposition in dual cones

Tobias Weth

DOI: http://dx.doi.org/10.12775/TMNA.2006.018

Abstract


We present an abstract approach to locate multiple solutions
of some superlinear
variational problems in a Hilbert space $H$. The approach
has many points in common with existing methods, but we add
a new tool by using a decomposition technique related to dual
cones in $H$ which goes back to Moreau.
As an application we deduce new existence
results for sign changing solutions for some
superlinear biharmonic boundary value problems.

Keywords


Flow invariant sets; multliple critical points; dual cone; sign changing solutions; biharmonic equations

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