This paper is devoted to study the positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations.The existence of positive solutions is established by using the fixed point theorem in cones. Mathematics Subject Classification: 34B15

This paper presents a new approach to the numerical solution of boundary value problems for higher index diierential algebraic equations. Invariants known for the original DAE as well as invariants of the reduced index 1 formulation are exploited to stabilize initial value problem integration, derivative generation and nonlinear and linear systems solution of an enhanced multiple shooting metho...

The existence of positive solutions for a class of singular third-order three-point boundary value problem is considered by using Guo-Krasnosel’skii fixed point theorem of cone expansion-compression type. In this class of problem, the nonlinear term is allowed to be singular. Main results show that this class of problem can have positive solutions provided that the conditions on the nonlinear t...

In this work we are concerned about singular boundary value problems for certain nonlinear second order ordinary differential equations on finite and infinite domains. An asymptotic expansion is obtained for the family of solutions satisfying the boundary condition at the origin. In the case of infinite domains, the asymptotic behavior of the solutions is also analysed for large values of the i...

Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The accuracy of the technique...

We investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems. Particular attention is paid to the well-posedness of the process. It is shown that boundary value problems can be solved efficiently when a high order integrator for the associated singular initial value problems is available. Moreover, convergence results for a perturbed...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...