Order BVPs Research Articles

A variational approach to the eigenvalue problem for higher order BVPs with singular nonlinearities

We present a variational approach to the eigenvalue problem for higher order equations with multipoint boundary conditions. Our approach covers the problems in which the nonlinearity may be singular at t=0 or t=1. The results can be applied for both sublinear and superlinear cases. We also describe the numerical characterization of positive solutions.

Coiflet–Galerkin method for solving second order BVPs with variable coefficients in three dimensions

Three dimensional BVPs with variable coefficients, need to evaluate a lot of complex integrals in Galerkin method solutions. We consider Coiflets, as basis functions to evaluate the complex integrals fast and effective, via three variate connection coefficients on the interval [0, 2n]. We show that these connection coefficients can be computed independent of n, by solving small linear systems. Moreover we prove that the rate of convergence of approximate solution to the exact solution, is O(2 − nN) where N is the degree of Coiflets. Besides, in our proposal we do not adopt fictitious domain approach which is commonly used in wavelet-Galerkin methods. In this way computational cost is reduced. To confirm the theoretical results, a numerical experiment is presented.

A Collocation Method for Global Approximation of General Second Order BVPs

For the numerical solution of the second order nonlinear two-point boundary value problems a family of polynomial global methods is derived.Numerical examples provide favorable comparisons with other existing methods.

Singular discrete second order BVPs with p-Laplacian

We study singular discrete boundary value problems with mixed boundary conditions and with the p-Laplacian of the form where , , , p>1. We assume that f is continuous on and has a singularity at x=0. We prove the existence of a positive solution by means of lower and upper functions method, Brouwer fixed point theorem and by a convergence of approximate regular problems.

A class of second order BVPs on infinite intervals

In this work, we are concerned with a boundary value problem associated with a generalized Fisher-like equation. This equation involves an eigenvalue and a parameter which may be viewed as a wave speed. According to the behavior of the nonlinear source term, existence results of bounded solutions, positive solutions, classical as well as weak solutions are provided. We mainly use fixed point arguments.

Sturm–Liouville and Focal Higher Order BVPs with Singularities in Phase Variables

Abstract The paper deals with the existence of solutions for singular higher order differential equations with Sturm–Liouville or (𝑝, 𝑛 – 𝑝) right focal boundary conditions or the (𝑛 – 𝑝, 𝑝) left focal boundary conditions. Right-hand sides of differential equations may be singular in the zero values of all their phase variables. The proofs are based on the regularization and sequential techniques.