A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Institution:	1. Department of Mathematics, Visva-Bharati University, Santiniketan 731235, India;2. Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India;1. Ryukyu Sankei Co. Ltd., 123 Maji, Naha, Okinawa, 902-0072, Japan;2. Okinawa Prefectural Plant Protection Center, 123 Maji, Naha, Okinawa, 902-0072, Japan;3. Graduate School of Agriculture, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Nakagami-gun, Okinawa, 903-0213, Japan

Abstract:	We consider the differential equation $- (1 / w) ({pu}^{'})^{'} + μ u = Fu$ , where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on $p, w, F$ and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

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