We discuss the existence and uniqueness of the solutions of a second-order m-point nonlocal boundary value problem by applying a generalized quasilinearization technique. A monotone sequence of solutions converging uniformly and quadratically to a unique solution of the problem is presented.

We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging quadratically to the unique solution of a general second order nonlinear differential equation with nonlinear nonlocal mixed three-point boundary conditions. The convergence of order n (n ≥ 2) of the sequence of iterates has also been established.

We study existence and approximation of solutions of some Neumann boundary-value problems in the presence of an upper solution β and a lower solution α in the reversed order (α ≥ β). We use the method of quasilinearization for the existence and approximation of solutions. We also discuss quadratic convergence of the sequence of approximants.

We study the existence of solutions for a periodic fourth order problem. We prove an associated uniform antimaximum principle and develop a method of upper and lower solutions in reversed order. Furthermore, by the quasilinearization method we construct an iterative sequence that converges quadratically to a solution.

The method of quasilinearization is applied to the nonlinear second order dynamic equations with m-point boundary conditions on time scales, and two sequences could be constructed which converge uniformly to the unique solution of the m-point boundary value problems from above and below with high rate of convergence. AMS Subject Classifications: 34B15, 39A12.

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of...

Abstract In this paper, we discuss the existence and approximation of solutions for a fourth-order nonlinear boundary value problem by using quasilinearization technique. presence lower solution α an upper β in reverse order $\alpha \geq \beta $ α ≥ β , show (extreme) solution.