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
, 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
Abstract.In this paper we consider a second order functional differential
equation
![\begin{displaymath}(r(t)x')' +
q(t)f\left(\max\limits_{s\in [\sigma (t),\tau (t)]}x(s)\right)=b(t),
\end{displaymath}](img5.png){kind=small}
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