A new approach to non-local boundary value problems for ordinary differential systems

Further results on the investigation of solutions of integral boundary value problems

“…To obtain the other required properties, similarly to [1] we will prove that under the con- Indeed, using the estimate (3.10) of Lemma1 for τ = a,…”

“…In this paper we use the technique suggested in [1] for the investigation of existence and approximate construction of solutions of a new class of non-linear boundary value problems with nonlinear integral boundary conditions involving the derivative. At first, we reduce the given problem to a simpler model problem with two-point separated linear parametrized boundary conditions.…”

Successive approximations and interval halving for integral boundary value problems

“…The aim of this paper is to show how a natural interval halving and parametrization technique can help to essentially improve the sufficient convergence conditions mentioned in papers [6], [9].…”

“…Note that in [6], [9], [5], [10] where the numerical-analytic approach was applied, instead of the previous inequality the convergence condition 2r.Q/ < 1: has appeared. Thus, the convergence condition is weakened by its half.…”

“…R n are a continuous functions in a certain bounded set D and d 2 R n is a given vector. We use an appropriate numerical-analytic approach and a natural interval halving technique which was suggested in [6], [4], [7], [8], [11], [3]. At first, we reduce the given problem (1.4), (1.5) To study the solutions of BVPs (1.6), (1.7) and (1.8), (1.9) we use the special modified form of parameterized successive approximations x m .t;´; / and y m .t; ; Á/ of type (1.3) constructed in analytic form and well defined on the intervals t 2 h a; a C i , respectively.…”