Positive Solution for a Hadamard Fractional Singular Boundary Value Problem of Order μ ∈(2,3)

In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hadamard fractional derivative of order μ. Moreover, the existence of positive solution has been established using fixed point index for a completely continuous map in a cone. Also, an example is included to show the validity of our result.

On the Existence of Positive Solution for n OrderSingular Boundary Value Problems

In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.

Numerical Solution of Quasilinear Singularly Perturbed Problems by the Principle of Equidistribution

In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed.

EXISTENCE OF POSITIVE SOLUTION TO NONLINEAR STURM-LIOUVILLE SINGULAR BVP

In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.

ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS

By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.