Existence of solutions for dynamic inclusions on time scales via duality

Abstract

The problem of 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 stay in the constraint set, are derived.

Submitted 29-Aug-2011; revised 09-Jan-2012; accepted 21-Jan-2012; for publication in Applied Mathematics Letters

References in corpus (10)

• Noether's Theorem on Time Scales
• Calculus of Variations on Time Scales with Nabla Derivatives
• Higher-Order Calculus of Variations on Time Scales
• Diamond-$\alpha$ Jensen's Inequality on Time Scales
• The Hahn Quantum Variational Calculus
• Isoperimetric problems on time scales with nabla derivatives
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Generalizing the variational theory on time scales to include the delta indefinite integral
• Euler-Lagrange equations for composition functionals in calculus of variations on time scales
• Backward Linear Control Systems on Time Scales

Cited by in corpus (5)

• Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales
• Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales
• Analysis of fractional integro-differential equations of thermistor type
• Direct and Inverse Variational Problems on Time Scales: A Survey
• Existence of Three Positive Solutions to Some $p$-Laplacian Boundary Value Problems