101 citations · 650 across the 25 of their papers we have counts for
4 papers · 1 filter
L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
Natalia Martins, Delfim F. M. Torres
We prove new l'Hopital rules for monotonicity valid on an arbitrary time scale. Both delta and nabla monotonic l'Hopital rules are obtained. As an example of application, we give s…
Noether's symmetry theorem for nabla problems of the calculus of variations
Natalia Martins, Delfim F. M. Torres
We prove a Noether-type symmetry theorem and a DuBois-Reymond necessary optimality condition for nabla problems of the calculus of variations on time scales.
The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
Zbigniew Bartosiewicz, Natalia Martins, Delfim F. M. Torres
The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. In th…
Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
Agnieszka B. Malinowska, Natalia Martins, Delfim F. M. Torres
We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and…