Dependence of a differential equation on the first eigenvalue of a suitable problem
Jan Bochenek (1980)
Annales Polonici Mathematici
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Jan Bochenek (1980)
Annales Polonici Mathematici
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Shmuel Friedland (2015)
Special Matrices
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In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.
Behrouz Emamizadeh, Amin Farjudian (2014)
Nonautonomous Dynamical Systems
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In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will...
Eberhard, W., Freiling, G., Schneider, A. (1992)
International Journal of Mathematics and Mathematical Sciences
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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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Muhic, Andrej, Plestenjak, Bor (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Qingliu Yao (2011)
Annales Polonici Mathematici
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This paper studies positive solutions and eigenvalue intervals of a nonlinear third-order two-point boundary value problem. The nonlinear term is allowed to be singular with respect to both the time and space variables. By constructing a proper cone and applying the Guo-Krasnosel'skii fixed point theorem, the eigenvalue intervals for which there exist one, two, three or infinitely many positive solutions are obtained.
Jan Bochenek (1971)
Annales Polonici Mathematici
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PrzemysŁaw Kosowski (1997)
Banach Center Publications
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The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
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.
Johann Walter (1973)
Mathematische Zeitschrift
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