Generalized transversality conditions for the Hahn quantum variational calculus. (English) Zbl 1262.39011
Summary: We prove optimality conditions for generalized quantum variational problems with a Lagrangian depending on the free end-points. Problems of calculus of variations of this type cannot be solved using the classical theory.
MSC:
39A13 | Difference equations, scaling (\(q\)-differences) |
39A70 | Difference operators |
49J05 | Existence theories for free problems in one independent variable |
49K05 | Optimality conditions for free problems in one independent variable |
49K15 | Optimality conditions for problems involving ordinary differential equations |
Keywords:
Hahn’s difference operator; Jackson-Norlünd’s integral; quantum calculus; calculus of variations; Euler-Lagrange equation; generalized natural boundary conditionsReferences:
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