The existence of solutions for dynamic inclusions on time scales via duality

Abstract The problem of the existence of solutions to nabla differential equations and nabla differential inclusions on time scales is considered. Under a special form of the set-valued constraint map, sufficient conditions for the existence of at least one solution, that stays in the constraint set, are derived.

[1]  Delfim F. M. Torres,et al.  Calculus of variations on time scales with nabla derivatives , 2008, 0807.2596.

[2]  Agnieszka B. Malinowska,et al.  The Hahn Quantum Variational Calculus , 2010, J. Optim. Theory Appl..

[3]  Delfim F. M. Torres,et al.  Generalizing the variational theory on time scales to include the delta indefinite integral , 2011, Comput. Math. Appl..

[4]  Delfim F. M. Torres,et al.  Noether's symmetry theorem for nabla problems of the calculus of variations , 2010, Appl. Math. Lett..

[5]  Agnieszka B. Malinowska,et al.  Strong minimizers of the calculus of variations on time scales and the Weierstrass condition , 2009, Proceedings of the Estonian Academy of Sciences.

[6]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

[7]  Agnieszka B. Malinowska,et al.  Euler-Lagrange equations for composition functionals in calculus of variations on time scales , 2010 .

[8]  Daniel C. Biles,et al.  First order dynamic inclusions on time scales , 2004 .

[9]  Delfim F. M. Torres,et al.  Higher-Order Calculus of Variations on Time Scales , 2007, 0706.3141.

[10]  V. Lakshmikantham,et al.  Dynamic systems on measure chains , 1996 .

[11]  Richard Bellman,et al.  Introduction to the mathematical theory of control processes , 1967 .

[12]  J. Diblík,et al.  Ważewski’s method for systems of dynamic equations on time scales , 2009 .

[13]  J. Aubin Set-valued analysis , 1990 .

[14]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[15]  S. Hilger Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[16]  Delfim F. M. Torres,et al.  Isoperimetric Problems on Time Scales with Nabla Derivatives , 2008, 0811.3650.

[17]  Shurong Sun,et al.  Existence of solutions for second-order dynamic inclusions , 2011 .

[18]  Ravi P. Agarwal,et al.  Dynamic equations on time scales: a survey , 2002 .

[19]  Ferhan Merdivenci Atici,et al.  An application of time scales to economics , 2006, Math. Comput. Model..

[20]  Delfim F. M. Torres,et al.  Diamond- Jensen's Inequality on Time Scales , 2007, 0712.1680.

[21]  D. Wishart Introduction to the Mathematical Theory of Control Processes. Volume 1—Linear Equations and Quadratic Criteria , 1969 .

[22]  Martin Bohner,et al.  Second Order Dynamic Inclusions , 2005 .

[23]  Agnieszka B. Malinowska,et al.  A general backwards calculus of variations via duality , 2010, Optim. Lett..

[24]  Delfim F. M. Torres,et al.  Backward linear control systems on time scales , 2010, Int. J. Control.

[25]  Delfim F. M. Torres,et al.  Avoidance Control on Time Scales , 2009, 0910.3308.

[26]  Time Scales : From Nabla Calculus to Delta Calculus and Vice Versa via Duality , 2010 .

[27]  Delfim F. M. Torres,et al.  Noether's theorem on time scales , 2008 .