Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems

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...

Singular Discrete Higher Order Boundary Value Problems

We study singular discrete nth order boundary value problems with mixed boundary conditions. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems. AMS subject classification: 39A10, 34B16.

Existence of Positive Solutions for Boundary-value Problems for Singular Higher-order Functional Differential Equations

We study the existence of positive solutions for the boundaryvalue problem of the singular higher-order functional differential equation (Ly(n−2))(t) + h(t)f(t, yt) = 0, for t ∈ [0, 1], y(0) = 0, 0 ≤ i ≤ n− 3, αy(n−2)(t)− βy(n−1)(t) = η(t), for t ∈ [−τ, 0], γy(n−2)(t) + δy(n−1)(t) = ξ(t), for t ∈ [1, 1 + a], where Ly := −(py′)′ + qy, p ∈ C([0, 1], (0,+∞)), and q ∈ C([0, 1], [0,+∞)). Our main to...

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

Existence and Uniqueness of Solutions for Singular Higher Order Continuous and Discrete Boundary Value Problems