where η ∈ (12 , 1) is a constant, g may be singular at t = 0 and/or 1. Moreover, F (t, u) may also have singularity at u = 0. The existence theorems of positive solutions for singular third-order third-point boundary value problems are obtained by using the first eigenvalue of the corresponding linear problems. Our results significantly extend and improve many known results including singular a...

Using the theory of fixed point theorem in cone, this paper presents the existence of positive solutions for the singular m-point boundary value problem

The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary partM(λ). We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoothness of M(λ) near its real roots permits us to describe the density of the singular spectrum. 20...

Based on a new explicit upper bound for the number of zeros of exponential polynomials in a horizontal strip, we obtain a uniform upper bound for the number of zeros of solutions to an ordinary differential equation near its Fuchsian singular point, provided that any two distinct characteristic exponents at this point have distinct real parts. The latter result implies that a Fuchsian different...

We investigate the number of limit cycles of a planar quadratic vector field with a perturbed center-like singular point. An upper bound is obtained on the number of δ-good limit cycles of such a vector field (Theorem 1). Here δ is a parameter characterizing the limit cycles: it shows how far those cycles are from the singular points of the vector field and from the infinite points. The bound a...

Accelerated and decelerated motions of a charged point particle inside medium are studied. It is shown explicitly that in addition to the bremsstrahlung and Cerenkov singular waves, previously unknown electromagnetic singular wave should be observed. It arises when the charge velocity coincides with the light velocity in medium. This wave has the same singularity as the Cerenkov one and, theref...

We obtain N = 1 SU(N) gauge theories with bifundamental matter and a quartic superpotential as the low energy theory on D3-branes at singular points. These theories generalize that on D3-branes at a conifold point, studied recently by Klebanov and Witten. For k = 3 the defining equation of the singular point is that of an isolated D4 singularity. For k > 3 we obtain a family of multimodular sin...

in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

In this paper, we propose a tailored-finite-point method for a type of linear singular perturbation problem in two dimensions. Our finite point method has been tailored to some particular properties of the problem. Therefore, our new method can achieve very high accuracy with very coarse mesh even for very small ε, i.e. the boundary layers and interior layers do not need to be resolved numerica...

In this paper we propose new blur identi cation algorithm based on singular value decomposition (SVD) of degraded image. An unknown space-invariant point-spread function (PSF) is also decomposed using SVD. Magnitude functions of PSF singular vectors (left and right) are identi ed using averaged spectra of corresponding singular vectors of degraded image. Phase functions of PSF singular vectors ...