


Paper's Title:
Construction of Lyapunov Functionals In Functional Differential Equations With Applications To Exponential Stability In Volterra Integrodifferential Equations
Author(s):
Youssef N. Raffoul
Department of Mathematics, University of Dayton,
Dayton OH 454692316,
USA
youssef.raffoul@notes.udayton.edu
URL:http://academic.udayton.edu/YoussefRaffoul
Abstract:
Nonnegative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee the exponential asymptotic stability and uniform exponential asymptotic stability of the zero solution of nonlinear functional differential systems. The theory is applied to Volterra integrodifferential equations in the form of proposition examples.
Paper's Title:
Positive Solution For Discrete ThreePoint Boundary Value Problems
Author(s):
WingSum Cheung And Jingli Ren
Department of Mathematics,
The University of Hong Kong,
Pokfulam, Hong Kong
wscheung@hku.hk
Institute of Systems Science,
Chinese Academy of Sciences,
Beijing 100080, P.R. China
renjl@mx.amss.ac.cn
Abstract:
This paper is concerned with the existence of positive solution to the discrete threepoint boundary value problem
_{
},
_{
}
where _{ }, and f is allowed to change sign. By constructing available operators, we shall apply the method of lower solution and the method of topology degree to obtain positive solution of the above problem for _{ } on a suitable interval. The associated Green’s function is first given.
Paper's Title:
Positive Periodic TimeScale Solutions for Functional Dynamic Equations
Author(s):
Douglas R. Anderson and Joan Hoffacker
Department of Mathematics and Computer Science
Concordia College
Moorhead, MN 56562 USA
andersod@cord.edu
URL: http://www.cord.edu/faculty/andersod/
Department of Mathematical Sciences
Clemson University
Clemson, SC 29634 USA
johoff@clemson.edu
URL: http://www.math.clemson.edu/facstaff/johoff.htm
Abstract:
Using Krasnoselskii's fixed point theorem, we establish the existence of positive periodic solutions to two pairs of related nonautonomous functional delta dynamic equations on periodic time scales, and then extend the discussion to higherdimensional equations. Two pairs of corresponding nabla equations are also provided in an analogous manner.
Paper's Title:
Positive Solutions for Systems of Threepoint Nonlinear Boundary Value Problems
Author(s):
J. Henderson and S. K. Ntouyas
Department of Mathematics, Baylor University
Waco, Texas
767987328 USA.
Johnny_Henderson@baylor.edu
URL: http://www3.baylor.edu/~Johnny_Henderson
Department of Mathematics, University of Ioannina
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas
Abstract:
Values of λ are determined for which there exist positive solutions of the system of threepoint boundary value problems, u''(t)+ λa(t)f(v(t))=0, v''(t)+λb(t)g(u(t))=0, for 0 < t <1, and satisfying, u(0) = 0, u(1)=α u(η), v(0) = 0, v(1)=α v(η). A GuoKrasnosel'skii fixed point theorem is applied.
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