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Explicit bounds on some retarded integral inequalities

Pachpatte B. G.

Fasciculi Mathematici

2005

Nr 35

85-98

In this paper we establish some new retarded integral inequalities which provide explicit bounds on unknown functions. Applications are also given to illustrate the usefulness of one of our results.

Integral inequalities associated with inequalities of Opial type

Florkiewicz B., Kuchta M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 1

41-45

We derive some new integral inequalities of the form: [...], h [belongs to] H, where I = (alpha, beta), -[infinity is less than or equal alpha < beta is less than or equal infinity], p > 0, H is a wide class of absolutely continuous functions h defined on I and satisfying the limit conditions h(alpha) = 0 or h(beta) = 0, the functions r, s and u are any set of functions related by the appropriate weight functions. To get the desired inequality, at first we derive an integral inequality of Opial type using a uniform method of obtaining integral inequalities with weight functions involving the function and its derivative [2].

Integral inequalities of Wirtinger and Opial type in three independent variables

Pachpatte B. G.

Fasciculi Mathematici

1999

Nr 30

113-129

In the present paper we establish some new Wirtinger and Opial type integral inequalities involving functions of three independent variables and their partial derivatives. The method used in the proof is elementary and our results provide new estimates on inequalities ofthis type.

Integral inequalities associated to the zeros of solutions of certain higher order differential equations

Pachpatte B. G.

Fasciculi Mathematici

1999

Nr 29

87-97

The aim of the present paper os to establish some new integra1 inequalities associated to the zeros of the solutions of certain higher order differential equations by using elementary analysis. The inequalities obtained here can be effectively used in the study of qualitative behavior of solutions of the corresponding equations.