On some fundamental integral inequalities and their discrete analogues. (English) Zbl 0989.26011

Pachpatte, B. G.

JIPAM, J. Inequal. Pure Appl. Math. 2, No. 2, Paper No. 15, 13 p. (2001).

Summary: The aim of the present paper is to establish some new integral inequalities in two independent variables and their discrete analogues which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential and finite difference equations.

MSC:

26D10	Inequalities involving derivatives and differential and integral operators
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
39A10	Additive difference equations

Keywords:

integral inequalities; discrete analogues; two independent variables; partial differential and difference equations; nondecreasing; nonincreasing; terminal value; non-selfadjoint hyperbolic partial differential equation