An eigenvalue problem for linear Hamiltonian dynamic systems

• Autorzy: Bohner M. , Hilscher R.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider eigenvalue problems on time scales involving linear Hainiltonian dynamic systems. We give conditions that ensure that the eigenvalues of the problem are isolated and bounded below. The presented results are applicable also to Sturm-Liouville dynamic equations of higher order, and further special cases of our systems are linear Hamiltonian differ ential systems as well as linear Hamiltonian difference systems.

Słowa kluczowe

EN

time scale; linear Hamiltonian system; eigenvalue; eigenfunction; quadratic functional; focal point; normality

PL

znajdowanie wartości własnych

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 35--49
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Bohner M.

• Department of Mathematics and Statistics, University of Missouri-Rolla, 115 Rolla Building, Rolla, MO 65409-0020, USA

autor

Hilscher R.

• Department of Mathematics, Michigan State University East Lansing, MI 48824-1027, USA

Bibliografia

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• [4] M. Bohner, Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions, J. Math. Anal. Appl., 199(3)(1996), 804-826.
• [5] M. Bohner, Discrete linear Hamiltonian eigenvalue problems, Comput. Math. Appl., 36(10-12)(1998), 179-192.
• [6] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
• [7] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
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• [9] R. Hilscher, Linear Hamiltonian systems on time scales: Positivity of quadratic functionals, Math. Comput. Modelling, 32(5-6)(2000), 507-527.
• [10] R. Hilscher, Inhomogeneous quadratic functionals on time scales, J. Math. Anal. Appl., 253(2)(2001), 473-481.
• [11] R. Hilscher, Positivity of quadratic functionals on time scales: Necessity, Math. Nachr., 226(1)(2001), 85-98.
• [12] B. Kaymakçalan, V. Lakshmikantham, S. Sivasundaram, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Boston, 1996.
• [13] W. Kratz, Quadratic Functionals in Variational Analysis and Control Theory, Akademie Verlag, Berlin, 1995.