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On a nonlinear Kirchhoff-Carrier wave equation in the unit membrane: the quadratic convergence and asymptotic expansion of solutions

Long N., Ngoc L.

Demonstratio Mathematica

2007

Vol. 40, nr 2

365-392

In this paper we consider the initial-boundary value problem for the nonlinear wave equation.

Extended method of quasilinearization for a nonlinear three-point boundary value problem

Ahmad B., Alsaedi A., Garout D.

Demonstratio Mathematica

2006

Vol. 39, nr 4

803-814

In this paper, we discuss the generalized quasilinearization technique for a second order nonlinear differential equation with nonlinear three-point general boundary conditions. In fact, we obtain sequences of upper and lower solutions converging mono- tonically and quadratically to the unique solution of the nonlinear three-point boundary value problem.