The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is considered. Based on a class of oscillator of ENSO model, the asymptotic solution of a corresponding problem is studied by employing the approximate method. It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model.
When φ is an analytic map of the unit disk D into itself, and X is a Banach space of analytic functions on D, define the composition operator Cφ by Cφ（f） ： f oφ, for f E X. This paper deals with a collection of subclasses of Bloch space by means of composition operators from a subspace B^0 of Qa to E（p,q） and Eo（p,q） and gets a new characterization of spaces E（p, q） and Eo（p, q）.
Let μ and v be normal functions and let Tg be the extended Ceshso operator in terms of the symbol g. In this paper, we will characterize those g so that Tg is bounded （or compact） from mixed norm spaces H（p, q, μ） to H（p, q, v） in the unit ball of C^n, Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces.
A class of singularly perturbed boundary value problems of weakly non linear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution and formal outer solution are constructed using the expansion method of power series. Secondly, using the transformation of stretched variable, the first boundary layer corrective term near x = a is constructed which possesses exponential attenuation behavior. Then, using the stronger transformation of stretched variable, the second boundary layer corrective term near x = a is constructed, wtfich also possesses exponential attenuation behavior. The thickness of second boundary layer is smaller than the first one and forms a cover layer near x = a. Finally, using the theory of differential inequalities, the existence, uniform validity in the whole interval [a, b] and asymptotic behavior of solution for the original boundary value problem are proved. Satisfying results are obtained.
