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We present some observations on the distribution of the zeros of solutions of the nonhomogeneous Airys equation. We show the existence of a principal family of solutions, with simple zeros, and particular solutions, characterized by a double zero in a given position of the complex plane. A recursion, describing the distribution of the zeros, is introduced and the limits of its applicability are discussed. The results can be considered a generalization of previous works on the distribution of the zeros for the solutions of the corresponding homogeneous equation
In this article, we study certain type of boundary behaviour of positive solutions of the heat equation on the upper half-space of $R^{n+1}$. We prove that the existence of the parabolic limit of a positive solution of the heat equation at a point in
We discuss some properties of Jacobi fields that do not involve assumptions on the curvature endomorphism. We compare indices of different spaces of Jacobi fields and give some applications to Riemannian geometry.
In this work we verify the sufficiency of a Jensens necessary and sufficient condition for a class of genus 0 or 1 entire functions to have only real zeros. They are Fourier transforms of even, positive, indefinitely differentiable, and very fast dec
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We derive the q-an
We study a new formulation for the eikonal equation |grad u| =1 on a bounded subset of R^2. Instead of a vector field grad u, we consider a field P of orthogonal projections on 1-dimensional subspaces, with div P in L^2. We prove existence and unique