Advances in Analysis

7

Authors: K.P.R.Rao, Sk.Sadik, S.V.K.Sarma

In this paper, we obtain a unique common coupled fixed point theorem for four self maps using property(E.A.)in complex valued b-metric spaces. Also we give an example to illustrate our main theorem.

10

Authors: P Sumati Kumari, I.Ramabhadra Sarma, J.Madhusudana Rao

In this paper, we intended to explain through some examples the usefulness and necessity of studying the topological properties of weaker forms of distance spaces.

21

Authors: Chaosheng Zhu

This paper is devoted to the large time behavior and especially to the regularity of the global attractor of the dissipative 1D nonlinear Schrödinger equation with nonlocal integral term on R. We first prove that the existence of the global attractor Aγ in the strong topology of H1 (R) and the existence of the exponential attractor M which contains the global attractor Aγ, are still finite dimensional, and attract the trajectories exponentially fast. We also show that the global attractor Aγ is regular, i.e., Aγ is included, bounded and compact in H2 (R) assuming that the forcing term f(x) is of class H2 (R). Furthermore we estimate the number of the determining modes for this equation. Moreover, we show that the solution trajectories and the global attractor of the nonlocal Schrödinger equation converge to those of the usual Schrödinger equation, as the coefficient of the nonlocal integral term goes to zero.