In the present article we are interested in the analysis of nonlocal initial boundary value problems for some medium oscillation equations. More precisely, we investigate different types of nonlocal problems for one-dimensional oscillation equations and prove existence and uniqueness theorems. In some cases algorithms for direct construction of the solution are given. We also consider nonlocal problem for multidimensional hyperbolic equation and prove the uniqueness theorem for the formulated initial boundary value problem applying the theory of characteristics under rather general assumptions.

By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for the Lotka-Volterra population model, considered by Song-Chen. [1], is established.

A theorem of Hardy asserts that a function and its Fourier transform cannot both be very small. We prove analogues of Hardy’s theorem for the Harish- Chandra transform for spherical functions on a non-compact semisimple Lie group and the Helgason transform on a Riemannian symmetric space of the non-compact type.

In this paper we consider an extended growth curve model with two hierarchical within-individuals design matrices, which is useful in analyzing mean profiles of several groups with parallel polynomial growth curves. The covariance structure based on a random e¤ects model is assumed. The maximum likelihood estimators (MLE’s) are obtained under the random e¤ects covariance structure. The efficiency of the MLE is discussed. A numerical example is also given.

The aim of this paper is to discuss a uniqueness property for Sobolev functions with certain condition on area integrals.

In this paper we give an application of quasimonotonicity methods and Bernstein functions to parabolic differential-functional equations in {$BUC({\bf R}\sp n,{\bf R})$}, and a new proof of the known result in Theorem 1 on solvability and asymptotic behaviour of its solutions.