Sturm-Liouville eigenvalue problems on time scales
Applied Mathematics and Computation
An application of time scales to economics
Mathematical and Computer Modelling: An International Journal
First order conditions for generalized variational problems over time scales
Computers & Mathematics with Applications
Time scale differential, integral, and variational embeddings of Lagrangian systems
Computers & Mathematics with Applications
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We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta derivative, but also on a delta indefinite integral that depends on the unknown function. Such kinds of variational problems were considered by Euler himself and have been recently investigated in [J. Gregory, Generalizing variational theory to include the indefinite integral, higher derivatives, and a variety of means as cost variables, Methods Appl. Anal. 15 (4) (2008) 427-435]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases.