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2004 On a variational characterization of a part of the Fučík spectrum and a superlinear equation for the Neumann $p$-Laplacian in dimension one
Eugenio Massa
Adv. Differential Equations 9(5-6): 699-720 (2004).

Abstract

In the first part of this paper a variational characterization of parts of the Fučík spectrum for the p-Laplacian in an interval is given. The proof uses a linking theorem on suitably constructed sets in $W^{1,p}(0,1)$. In the second part, a superlinear equation with Neumann boundary conditions on an interval is considered, where the nonlinearity intersects all but the first eigenvalues. It is proved that under certain conditions this equation is solvable for arbitrary forcing terms. The proof uses a comparison of the minimax levels of the functional associated to this equation with suitable minimax values related to the Fučík spectrum.

Citation

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Eugenio Massa. "On a variational characterization of a part of the Fučík spectrum and a superlinear equation for the Neumann $p$-Laplacian in dimension one." Adv. Differential Equations 9 (5-6) 699 - 720, 2004.

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1111.34061
MathSciNet: MR2099977

Subjects:
Primary: 34L30
Secondary: 47J30, 49J35

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 5-6 • 2004
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