The variational calculus on time scales
نویسندگان
چکیده
منابع مشابه
The Variational Calculus on Time Scales
Abstract. The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we review a more genera...
متن کاملThe Second Euler-Lagrange Equation of Variational Calculus on Time Scales
The fundamental problem of the calculus of variations on time scales concerns the minimization of a deltaintegral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the main result, we give an alternative and si...
متن کاملRemarks on the calculus of variations on time scales
The calculus of variations is a classical subject which has gain throughout the last three hundred years a level of rigor and elegance that only time can give. In this note we show that, contrary to the classical field, available formulations and results on the recent calculus of variations on time scales are still at the heuristic level.
متن کاملIsoperimetric Problems of the Calculus of Variations on Time Scales
We prove a necessary optimality condition for isoperimetric problems on time scales in the space of delta-differentiable functions with rdcontinuous derivatives. The results are then applied to Sturm-Liouville eigenvalue problems on time scales.
متن کاملVariational Methods for Two Resonant Problems on Time Scales∗
Using variational methods we study the generalization of two classical second order periodic problems in the context of time scales. On the one hand, we study a forced pendulum-type equation. On the other hand, we obtain solutions for a bounded nonlinearity under Landesman–Lazer type conditions. AMS subject classification: 39A12, 39A99.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal for Simulation and Multidisciplinary Design Optimization
سال: 2010
ISSN: 1779-627X,1779-6288
DOI: 10.1051/ijsmdo/2010003