Necessary optimality conditions for the calculus of variations on time scales

We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems of the calculus of variations with delta-differential side conditions (Lagrange problem of the calculus of variations on time scales).

💡 Research Summary

The paper “Necessary optimality conditions for the calculus of variations on time scales” extends the calculus of variations on arbitrary time scales by deriving necessary optimality conditions for two broader classes of problems. First, it treats variational problems whose Lagrangian depends on higher‑order delta derivatives yΔ, yΔ², …, yΔʳ (r ≥ 1). By working in the function space Cʳʳᵈ