An iterative method for a class of quasilinear boundary value problems

Authors:
Qingliu Yao
Affiliations:
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Let n=3. In this paper, we consider the following general quasilinear boundary value problem of second order {u^''(t)+n-1tu^'(t)+f(t,u(t))=0,a.e.t@?[0,1],u^'(0)=0,u(1)=0, where the nonlinear term f(t,u) is a strong Caratheodory function. By applying the monotonically iterative technique, we construct a sequence of successive approximations and prove that the sequence converges uniformly to the solution of the above problem under suitable assumptions.