By means of some Picone-type identity, we provide some simple oscillation criteria for the equations { a(t)φα(y ′) }′ + q(t)φβ(h(y)) = 0, t > 0; α, β > 0. Mathematics Subject Classification: 34C10, 34K15
We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and perfor...
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward. The method, whose mathematical basis in physics was discussed recently by one of the present ...
