The delta-nabla calculus of variations

• Autorzy: Malinowska A. B. , Torres D. F. M.
• Języki publikacji: EN

Abstrakty

EN

The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla results as particular cases.

Słowa kluczowe

EN

Euler-Lagrange equations; calculus of variations; time scales

PL

rachunek wariacyjny; skala czasu; równania Eulera-Lagrange'a

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 44
• Strony: 75--83
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Malinowska A. B.

autor

Torres D. F. M.

• Faculty of Computer Science Białystok University of Technology 15-351 Białystok, Poland,

Bibliografia

• [1] Almeida R., Torres D.F.M., Isoperimetric problems on time scales with nabla derivatives, J. Vib. Control, 15(6)(2009), 951-958.
• [2] Atici F.M., Biles D.C., Lebedinsky A., An application of time scales to economics, Math. Comput. Modelling, 43(7-8)(2006), 718-726.
• [3] Atici F.M., Guseinov G.S., On Green’s functions and positive solutions for boundary value problems on time scales. Dynamic equations on time scales, J. Comput. Appl. Math., 141(1-2)(2002), 75-99.
• [4] Atici F.M., McMahan C.S., A comparison in the theory of calculus of variations on time scales with an application to the Ramsey model, Nonlinear Dyn. Syst. Theory, 9(1)(2009), 1-10.
• [5] Atici F.M., Uysal F., A production-inventory model of HMMS on time scales, Appl. Math. Lett., 21(3)(2008), 236–243.
• [6] Bartosiewicz Z., Torres D.F.M., Noether’s theorem on time scales, J. Math. Anal. Appl., 342(2)(2008), 1220-1226.
• [7] Bohner M., Calculus of variations on time scales, Dynam. Systems Appl., 13(3-4)(2004), 339-349.
• [8] Bohner M., Peterson A., Dynamic equations on time scales. An introduction with applications, Birkhäuser Boston, Inc., Boston, MA, 2001.
• [9] Castillo E., Luceo A., Pedregal P., Composition functionals in calculus of variations. Application to products and quotients, Math. Models Methods Appl. Sci., 18(1)(2008), 47-75.
• [10] Gürses M, Guseinov G.Sh., Silindir B., Integrable equations on time scales, J. Math. Phys., 46(11)(2005), 113510, 22 pp.
• [11] Martins N., Torres D.F.M., Calculus of variations on time scales with nabla derivatives, Nonlinear Anal., 71(12)(2009), e763-e773.