Document Zbl 0809.26010

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Pachpatte, B. G.

On some new discrete inequalities related to a certain integral inequality. (English) Zbl 0809.26010

Libertas Math. 13, 85-97 (1993).

In the notations of the preceding review, the author considers inequalities \[ u(n)\leq \{c+ T(n,k,r; F(i,u(i)))\}^{1/2} \] with \(F(i,u(i))= f(i) u(i)\). Furthermore, some special cases of systems with two unknown functions \(u_ 1(n)\), \(u_ 2(n)\) are studied. As an example of possible applications of the obtained results, the author gives bounds for the solutions of the equation \[ \Delta^{n_ 2}_ 2 \Delta^{n_ 1}_ 1[u(x_ 1, x_ 2)]^ 2= f(x_ 1,x_ 2,u(x_ 1, x_ 2)). \] {}.

Reviewer: J.Popenda (Poznań)

Cited in 1 Review

Cited in 1 Document

MSC:

26D15	Inequalities for sums, series and integrals
39A12	Discrete version of topics in analysis

Keywords:

finite difference inequalities; Gronwall inequality

Citations:

Zbl 0809.26009

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