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We study global asymptotic behavior of Poisson-Nernst-Planck (PNP) systems for flow of two ion species through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from… (More)

- Pedro Martınez-Amores, Pedro J. Torres, Jack K. Hale
- 1996

Feedback systems are important in applications, for example, optical feedback lasers, phase-locked frequency synthesizers and wave equations with feedback stabilization at the boundary, and the problem regarding sensitivity and robustness of the feedback system with respect to time delays has attracted a lot of attention. In this paper we continue the… (More)

- Yingfei Yi, Wenxian Shen, G. Hetzer, R. Ellis, R. A. Johnson, G. R. Sell +11 others

- Jack K. Hale, J. Mawhin
- 2008

- Bogdan Przeradzki, Robert Stanczy, Jack K. Hale
- 2001

This paper is concerned with the problem of existence of a solution for the multi-point boundary value problem, k xЉ t s f t, x t , xЈ t , 0-t-1, x 0 s 0, x 1 s x ,

We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction… (More)

We consider the quasilinear problem −ε p div(|∇u| p−2 ∇u) + V (z)u p−1 = f (u) + u p * −1 , u ∈ W 1,p (R N), where ε > 0 is a small parameter, 1 < p < N , p * = N p/(N − p), V is a positive potential and f is a superlinear function. Under a local condition for V we relate the number of positive solutions with the topology of the set where V attains its… (More)

- Jack K. Hale
- 2007

We present a study on the critical time step for the numerical integration based on the Runge-Kutta method of the monodromy matrix (the fundamental matrix solution) associated with a set of n rst-order linear ordinary diierential equations with periodic coeecients. By applying the Liapunov-Schmidt method, for any dimension n and systems which are… (More)

DEDICATION I dedicate this thesis to my wife, Semra. Tech. I will never forget his help and support. In this respect, I want to thank Professors M. Akhmet and O. Celebi for their support during my studies there. Many special thanks to my loving wife Semra. She has encouraged me, pushed me and put up with me during my studies. I feel very lucky to have such… (More)

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