IJPAM: Volume 63, No. 3 (2010)
DIFFERENTIAL EQUATION WITH ``MAXIMA"
Department of Mathematics
University of Chemical Technology and Metallurgy
8, Kliment Ohridski Blvd., Sofia, 1756, BULGARIA
e-mail: firstname.lastname@example.org, email@example.com
url: https://math.uctm.edu/ mkolev
Department of Mathematics, Physics and Chemistry
Sliven, 8800, BULGARIA
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