Spectral asymptotics for Hill's equation near the potential maximum

Inverse scattering problem for the Impulsive Schrodinger equation with a polynomial spectral dependence in the potential

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...

The spectral iterative method for Solving Fractional-Order Logistic ‎Equation

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

Asymptotics for the biharmonic equation near the tip of a crack

Spectral asymptotics for canonical systems

Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl–Titchmarsh and spectral functions of 2×2 first order canonical systems. Our results improve several classical results and solve open problems posed by previous authors. Furthermore, they are applied to radial Dirac and radial Schrödinger operators as well as to Kr...

Fine Asymptotics near Extinction and Elliptic Harnack Inequalities for the Fast Diffusion Equation

We consider the Fast Diffusion Equation (FDE) ut = ∆u in a bounded smooth domain Ω ⊂ R with homogeneous Dirichlet conditions; the exponent range is ms = (d − 2)+/(d + 2) < m < 1. It is known that bounded positive solutions u(t, x) of such problem extinguish in a finite time T , and also that such solutions approach a separate variable solution u(t, x) ∼ (T − t)1/(1−m)f(x), as t → T−. We show th...