In this paper we study Dirichlet boundary-value problems, for the p-Laplacian, of the form
where is a bounded domain with smooth boundary , , and is the first eigenvalue of . We study the geometry of the energy functional
and show the difference between the case and the case . We also give the characterization of the right hand sides for which the Dirichlet problem above is solvable and has multiple solutions.
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|Pavel Drabek |
Centre of Applied Mathematics
University of West Bohemia
P. O. Box 314, 306 14 Plzen, Czech Republic
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