### A Series Method for Solving Nonlinear Two-Point Boundary Value Problems.

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By means of the reduction of boundary value problems to algebraic ones, conditions for the existence of solutions and explicit expressions of them are obtained. These boundary value problems are related to the second order operator differential equation X(2) + A1X(1) + A0X = 0, and X(1) = A + BX + XC. For the finite-dimensional case, computable expressions of the solutions are given.

We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic.

An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.

We apply the method of quasilinearization to multipoint boundary value problems for ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic.

The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.