Consider the following nonlinear delay differential equation with a forcing term r(t) : x′(t)+a(t)x(t)+b(t) f (x(t − τ(t))) = r(t), t 0, where a ∈ C[[0,∞), [0,∞)] , b,τ ∈C[[0,∞),(0,∞)] , r ∈C[[0,∞),R] , f ∈ C[(L,∞),(L,∞)] with −∞ L 0 , and limt→∞(t − τ(t)) = ∞ . We establish a sufficient condition for every solution of the equation to converge to zero. By applying the result to some special cas...

By using the averaging technique, some integral oscillation criteria are obtained for even order damped delay differential equations. 1 – Introduction This paper deals with the oscillatory behavior of the even order damped delay differential equation (1.1) ( Φ(xn−1)(t)) )′ + p(t)Φ(x(n−1)(t)) + f ( t, x[ τ01(t) ], ..., x[ τ0m(t) ], ..., x(n−1)[ τn−11(t) ], ..., x (n−1)[ τn−1m(t) ] ) = 0 for t ≥ ...

BACKGROUND Classically, the ST-T configuration in the electrocardiogram of patients with left ventricular hypertrophy is said to have a typical pattern of ST depression together with asymmetrical T wave inversion (the so-called left ventricular strain pattern). However, many patients with left ventricular hypertrophy may also have ischaemic heart disease. To revise the electrocardiographic crit...

By using a multiple fixed point theorem Avery-Peterson fixed point theorem for cones, some criteria are established for the existence of three positive periodic solutions for a class of higherdimensional functional differential equations with impulses on time scales of the following form: xΔ t A t x t f t, xt , t / tj , t ∈ T, x t j x tj Ij x tj , where A t aij t n×n is a nonsingular matrix wit...

In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation ( r(t) (( y(t)+ p(t)y(t − τ))∆)γ )∆ + f (t, y(t − δ))= 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r(t) and p(t) real-valued positive functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of the...

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability decision theory methods. Multiple-criteria making (MCDM) very effective well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be done utilizing symmetry because enterprises do not have comple...

A phase transition is a jump discontinuity in a solution u to (1.1) between states u(t, x−) and u(t, x+) belonging to different phases. Physical models leading to this setting are provided by liquid vapor phase transitions, elastodynamics or combustion models, see [2, 7, 8, 9, 19, 20] and the references therein. Typically, in the case (1.2) the Riemann problem for (1.1) turns out to be underdet...