# IJPAM: Volume 63, No. 3 (2010)

**NONOSCILLATION OF A SECOND ORDER SUBLINEAR**

DIFFERENTIAL EQUATION WITH ``MAXIMA"

DIFFERENTIAL EQUATION WITH ``MAXIMA"

D. Kolev, N. Markova, S. Nenov

Department of Mathematics

University of Chemical Technology and Metallurgy

8, Kliment Ohridski Blvd., Sofia, 1756, BULGARIA

e-mail: mkolev@math.uctm.edu, kolev@uctm.edu

url: https://math.uctm.edu/ mkolev

e-mail: svety@math.uctm.edu

Department of Mathematics, Physics and Chemistry

Technical University

Sliven, 8800, BULGARIA

e-mail: n_markova54@abv.bg

Department of Mathematics

University of Chemical Technology and Metallurgy

8, Kliment Ohridski Blvd., Sofia, 1756, BULGARIA

e-mail: mkolev@math.uctm.edu, kolev@uctm.edu

url: https://math.uctm.edu/ mkolev

e-mail: svety@math.uctm.edu

Department of Mathematics, Physics and Chemistry

Technical University

Sliven, 8800, BULGARIA

e-mail: n_markova54@abv.bg

**Abstract.**In this paper we consider a second order functional differential
equation

containing a function of sublinear rate and depending on the maximum of the unknown and defined on some interval taken before coming the present time . We call this equation with ``maxima". Criteria for existence of nonoscillating solutions are established under requirement that , , , should be continuous on some sets, and has sublinear rate. These differential equations could be seen in lots of mathematical models in theoretical physics, optimal control, chemistry, mechanics of materials, biology, ecology, etc.

**Received: **May 20, 2010

**AMS Subject Classification: **34K15

**Key Words and Phrases: **differential equations with ``maxima'', second order ODEs, sublinear differential equation, nonoscillation, oscillation

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2010

**Volume:** 63

**Issue:** 3