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.

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

The method of quasilinearization coupled with the method of lower and upper solutions is applied to systems of nonlinear differential equations with a singular matrix. It generates sequences of approximate solutions which are convergent to the solution and the convergence is quadratic or semiquadratic.

The quasilinearization method coupled with the method of upper and lower solutions is used for a class of nonlinear boundary value problems with integral boundary conditions. We obtain some less restrictive sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem. An example is also included to illustrate the m...