Boundary value problems for differential equations with reflection of the argument

Linear and nonlinear boundary value problems for differential equations with reflection of the argument are considered

On the stability of solutions of certain systems of differential equations with piecewise constant argument

summary:We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument

Highly degenerate parabolic boundary value problems

Of concern are parabolic equations of the form ∂u/∂t = φ(x, ∇u)Δu (x ∈ Ω ⊂ Rn, t ≥ 0) where φ(x, ξ) \u3e 0 on Ω X Rn but φ(x, ξ) → 0 very rapidly as X → ∂Ω. By associating the Wentzel boundary condition with this equation, the initial value problem is shown to be well-posed. This is done with the aid of the Crandall-Liggett theorem, applied in the space C(Ω). © 1989, Khayyam Publishing. All rights reserved

T-periodic solutions for a second order system with singular nonlinearity

We consider a system of the form u’' + au’ = Hv(u, v)-h(t) v’' + bv’ = Hu(u, v)-k(t), where h, k are locally integrable and T-periodic, and H is a C1 function defined on (0,∞)x(0,∞), for which a good model is given by H(u, v) =-(1/uα + 1/vβ),α,β, > 0. We state conditions under which existence of positive, T-periodic solutions for this system is ensured. We also study the problems of uniqueness and existence of multiple solutions in some special cases. © 1995, Khayyam Publishing

On a logistic equation with piecewise constant arguments

Let [·] denote the greatest-integer function and consider the logistic equation with piecewise constant arguments (*) where r ∈ (0, ∞) and ao, a1, · · ·, am ∈ [0, ∞) Σmj=0 aj \u3e 0 and r+m ≠ 1. We obtained necessary and sufficient conditions for the oscillation of all positive solutions of equation (*) about the positive steady state N* = Σmj=0aj) -1. We also obtained sufficient conditions for the global attractivity of the positive steady state N*. © 1991, Khayyam Publishing. All rights reserved