Weak solutions of functional differential inequalities with first-order partial derivatives

• Published in: Journal of inequalities and applications Vol. 2011; no. 1; pp. 1 - 20
• Main Author: Kamont, Zdzisław
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 22.06.2011; Springer Nature B.V; BioMed Central Ltd; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Classification; Comparison theorems; Derivatives; Differential equations; Functional differential inequalities; Functions (mathematics); Haar pyramid; Inequalities; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Theorems; Weak solutions of initial problems; Haar pyramid; Functional differential inequalities; Comparison theorems; Weak solutions of initial problems
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/1029-242X-2011-15

The article deals with functional differential inequalities generated by the Cauchy problem for nonlinear first-order partial functional differential equations. The unknown function is the functional variable in equation and inequalities, and the partial derivatives appear in a classical sense. Theorems on weak solutions to functional differential inequalities are presented. Moreover, a comparison theorem gives an estimate for functions of several variables by means of functions of one variable which are solutions of ordinary differential equations or inequalities. It is shown that there are solutions of initial problems defined on the Haar pyramid. Mathematics Subject Classification: 35R10, 35R45 .