In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

In this paper, the solution of a moving Volterra-type screw dislocation in an orthotropic layer, bonded between two piezoelectric layers is obtained using complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple moving cracks. These equations, which are classified as, Cauchy singular equations, ...

In the present paper the linear oscillator in R3 with z =constanthas been considered. The aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. A newapproach based on a computational method has been used. At the end weapply our method on an example.

In this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. Nonlinear system affected by an periodic external source is studied. Existence of a control variable provides  the extension of  some previous results obtained in other studies. We give a illustrative e...

We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations. Such problems arise in the solution process of incompressible Navier–Stokes equations and in the time-harmonic wave propagation in the frequence space with the zero wavenumber. The equation is first discretized with a fourth order modified Collatz difference scheme, producing a si...

Each D A microarray experiment generates a large amount of gene expression profiles and it remains a challenge for biologists to robustly identify periodic gene expression profiles with certain noise level in the data. In this paper, we propose a new scheme with noise filtering technique to analyze the periodicity of gene expression base on singular value decomposition (SVD), singular spectrum ...

We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this a...

The Klein–Fock–Gordon equation (KFGE), defined as the of relativistic wave related to NLEEs, has numerous implications for energy particle physics and is useful a model several types matter, with deviation in basic stuffs particles crystals. In this work, Sardar subequation method (SSM) used finding solution KFGE. advantage SSM that it provides many different kinds solitons, such dark, bright, ...

‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...