On partial differential inequalities of the first order with a retarded argument

  • Zdzisław Kamont

    University of Gdansk, Poland
  • Stanisław Zacharek

    Technical University of Gdansk, Poland

Abstract

This paper deals with first order partial differential inequalities of the form

where and

We assume that (i) is of the Volterra type. Let

and

Assume that satisfy on the Lipschitz condition with respect to . Suppose that and satisfy almost everywhere on the differential inequalities

and the initial inequality on . In the paper we prove that under certain assumptions concerning the functions , the inequality is satisfied on .

Cite this article

Zdzisław Kamont, Stanisław Zacharek, On partial differential inequalities of the first order with a retarded argument. Z. Anal. Anwend. 2 (1983), no. 2, pp. 135–144

DOI 10.4171/ZAA/55