In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties eigenvalues and eigenfunctions for the strongly elliptic operator then obtain two existence theorems nontrivial solutions when nonlinearity is function with an asymptotically condition.

Abstract: This study is carried out to describe the behaviour of vehicles flow on the road, in the presence of blocking effects. A non-linear three dimensional system of ordinary differential equations is used to describe vehicles flow on the road. The study classify total vehicles population on the road into three compartments as Free – Slow – Released vehicles. The formulated model is well-po...

A commonly used semiparametric partial linear model is considered. We propose analyzing this model using a difference based approach. The procedure estimates the linear component based on the differences of the observations and then estimates the nonparametric component by either a kernel or a wavelet thresholding method using the residuals of the linear fit. It is shown that both the estimator...

In this paper, we study the following nonlinear elliptic problem -div(a(x) ?u) = f (x,u), x ? u H10(?) (P) where is a regular bounded domain in RN, N 2, a(x) positive function and reaction source strongly asymptotically linear sense lim t?+? f(x,t)/t q(x) uniformly ?. We use variant version of Mountain Pass Theorem to prove that has solution for large class (x,t) q(x). Here, existence proved wi...

The problem of quickest detection of an anomalous process among M processes is considered. At each time, a subset of the processes can be observed, and the observations from each chosen process follow two different distributions, depending on whether the process is normal or abnormal. The objective is a sequential search strategy that minimizes the expected detection time subject to an error pr...

A two-grid discretization scheme is proposed for solving eigenvalue problems, including both partial differential equations and integral equations. With this new scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid, and the solution of a linear algebraic system on the fine grid and the resulting solution still ma...

For network revenue management problems, it is known that the bid prices computed through the socalled deterministic linear program are asymptotically optimal as the capacities on the flight legs and the expected numbers of product requests increase linearly with the same rate. In this paper, we show that the same asymptotic optimality result holds for the bid prices computed through the so-cal...