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Variational calculus on \(q\)-nonuniform lattices. (English) Zbl 1095.49005

The main aim of the present paper is to present the \(q\)-version of the variational calculus in the general non-uniform lattices (non \(q\)-linear lattices). In fact this paper is the logical continuation of the preceding paper “Variational \(q\)-calculus” [J. Math. Anal. Appl. 289, No. 2, 650–665 (2004; Zbl 1043.49001)] by the same author. In this paper the author obtains the \(q\)-analog of the Euler-Lagrange equation for non-uniform lattices and applies this to several problems as the isoperimetric, Lagrange and the optimal control problems on non-uniform lattices.

MSC:

49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
39A13 Difference equations, scaling (\(q\)-differences)

Citations:

Zbl 1043.49001
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References:

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