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- W2092963999 abstract "In this paper we provide a survey of characterizations of the nonnegativity and positivity of discrete quadratic functionals which arise as the second variation for nonlinear discrete calculus of variations problems. These characterizations are in terms of (i) (strict) conjugate and (strict) coupled intervals, (ii) the conjoined bases of the associated Jacobi difference equation, and (iii) the solution of the corresponding Riccati difference equation. The results depend on the form of the boundary conditions of the quadratic functional and, basically, we distinguish three types: (a) separable endpoints with zero right endpoint (this of course includes the simplest case of both zero endpoints), (b) separable endpoints, and (c) jointly varying endpoints." @default.
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- W2092963999 date "2005-08-01" @default.
- W2092963999 modified "2023-09-27" @default.
- W2092963999 title "Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey" @default.
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- W2092963999 doi "https://doi.org/10.1080/10236190500137454" @default.
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