in this paper we consider the second order nonlinear neutral delay partial difference equation $delta_ndelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$under suitable conditions, by making use of the banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

This is a rough historical account of some uses of the Lefschetz Principle in fixed point theory and index theory. The Lefschetz Principle states that the alternating sum of the traces on cohomology (a global and rigid invariant) is equal to the alternating sum of the traces on the underlying cochain complex (a local and far less rigid invariant). The original Lefschetz Theorem for compact poly...

The development of the study of periodic solution of functional difference equations is relatively rapid. There has been many approaches to study periodic solutions of difference equations, such as critical point theory, fixed point theorems in Banach spaces or in cones of Banach spaces, coincidence degree theory, KaplanYorke method, and so on, one may see [3-7,11,13-15] and the references ther...

We consider classes of second order boundary value problems with a nonlinearity f (t, x) in the equations and subject to a multi-point boundary condition. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. The symmetry of solutions is also studied. Conditions are determined by the relationship betwe...

This paper is devoted to investigate the existence of positive periodic solution for a functional differential equation in the form of λLx = −b(t) f (x(t − τ(t))), where Lx = x ′ (t) − a(t)g(x(t))x(t). By using well-known fixed point index theory in a cone, values of λ are determined for which there exist positive periodic solutions for the above functional differential equation. The dependence...

in an ordered Banach space E with positive cone K, where M >0 is a constant, f : [0, 1] × K × K ® K is continuous, S : C([0, 1], K) ® C([0, 1], K) is a Fredholm integral operator with positive kernel. Under more general order conditions and measure of noncompactness conditions on the nonlinear term f, criteria on existence of positive solutions are obtained. The argument is based on the fixed p...

Received: 09 Mar. 2012; Revised 23 Jul. 2012; Accepted 02 Sep. 2012 Received: May 8, 2012; Revised June 1, 2012; Accepted June 5, 2012 Abstract: In this paper, we’ll give some new conclusion of fixed point related to the multi-valued map, the calculation of fixed point index, and the solutions to nonlinear equations by using VIM. We apply the effective modification of its variation iteration me...

Recommended by Alberto Cabada Criteria are established for existence of least one or three positive solutions for boundary value problems of second-order functional dynamic equations on time scales. By this purpose, we use a fixed-point index theorem in cones and Leggett-Williams fixed-point theorem.