Singular and nonsingularizable higher-order differential matrix equations

Singular Higher Order Boundary Value Problems for Ordinary Differential Equations

This paper is somewhat of an extension of the recent work done by Kunkel [6]. Kunkel looked at an extension of Rachu̇nková and Rachu̇nek’s work where they studied a second order singular boundary value problem for the discrete p-Laplacian, φp(x) = |x|x [7]. Kunkel’s results extend theirs to the second order differential case, but only for p = 2, i.e. φ2(x) = x. In this paper, we extend Kunkel’s w...

First-Order Singular and Discontinuous Differential Equations

Singular Sets of Higher Order Elliptic Equations

The implicit function theorem implies that the zero set of a smooth function, the set where the function vanishes, is a smooth hypersurface away from the critical zero set. Hence to study zero sets it is important to understand the structure of the critical zero sets. For solutions of the second order elliptic equations the critical zero sets represent the singular parts of zero sets. They have...

Semipositone higher-order differential equations

Krasnoselskii’s fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone conjugate and (n, p) problems. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Existence, Positive solution, Semipositone, Conjugate and (n,p) problems.

Painlevé Test and Higher Order Differential Equations

Starting from the second Painlevé equation, we obtain Painlevé type equations of higher order by using the singular point analysis.