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On the existence of global solutions of evolution equations

Medved M.

Demonstratio Mathematica

2004

Vol. 37, nr 4

871--882

In this paper a sufficient condition for the existence of global solutions of evolution equations is proved. In the proof a modification of the Bihari type integral inequality to the case of a weakly singular nonlinear integral inequality is used. An application to a reaction-diffusion problem is given.

New Ostrowski type inequalities for mappings whose derivatives belong to Lp spaces

Pachpatte B.

Demonstratio Mathematica

2004

Vol. 37, nr 2

293--298

The aim of the present paper is to establish two new Ostrowski type inequalities for mappings whose derivatives belongs to Lp -spaces. The analysis used in the proofs is elementary and our results in the special cases yields the Ostrowski type inequality recently established by Dragomir and Wang.

Qualitative behaviour of an integral equation related to some epidemic model

Brestovanská E.

Demonstratio Mathematica

2003

Vol. 36, nr 3

603--609

Sufficient conditions for the uniqueness, global existence and for the convergence to zero when t -> oo of solutions of an integral equation related to an epidemic model are proved. The existence result is proved by applying the Banach fixed point theorem and for the proof of the convergence result a new type of integral inequality is used.