Eigenfunction expansion for a regular fourth order eigenvalue problem with eigenvalue parameter in the boundary conditions.
Zayed, E.M.E., Ibrahim, S.F.M. (1989)
International Journal of Mathematics and Mathematical Sciences
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Zayed, E.M.E., Ibrahim, S.F.M. (1989)
International Journal of Mathematics and Mathematical Sciences
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Zayed, E.M.E., Ibrahim, S.F.M. (1990)
International Journal of Mathematics and Mathematical Sciences
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Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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O. A. Olejnik (1989)
Journées équations aux dérivées partielles
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Eastham, M.S.P., Kong, Q., Wu, H., Zettl, A. (1999)
Journal of Inequalities and Applications [electronic only]
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Afrouzi, G.A. (2002)
International Journal of Mathematics and Mathematical Sciences
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W. Weinelt (1974)
Acta Universitatis Carolinae. Mathematica et Physica
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J. Fleckinger, J. Hernández, F. Thélin (2004)
Bollettino dell'Unione Matematica Italiana
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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.