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A multiplicity theorem for problems with the p-Laplacian
Authors:Evgenia H. Papageorgiou
Affiliation:Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Abstract:We consider a nonlinear elliptic problem driven by the p-Laplacian, with a parameter λR and a nonlinearity exhibiting a superlinear behavior both at zero and at infinity. We show that if the parameter λ is bigger than λ2=the second eigenvalue of View the MathML source, then the problem has at least three nontrivial solutions. Our approach combines the method of upper-lower solutions with variational techniques involving the Second Deformation Theorem. The multiplicity result that we prove extends an earlier semilinear (i.e. p=2) result due to Struwe [M. Struwe, Variational Methods, Springer-Verlag, Berlin, 1990].
Keywords:Multiple nontrivial solutions   Superlinear nonlinearity   Upper and lower solutions   Eigenvalues of the p-Laplacian   Second deformation theorem
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