Monotone method for singular BVP in the presence of upper and lower solutions |
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Authors: | RK Pandey Amit K Verma |
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Institution: | a Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, India b Mathematics Group, BITS Pilani, Pilani 333 031, Rajasthan, India |
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Abstract: | In this paper we examine existence of monotone approximations of solutions of singular boundary value problem -(p(x)y′(x))′=q(x)f(x,y,py′) for 0<x?b and limx→0+p(x)y′(x)=0,α1y(b)+β1p(b)y′(b)=γ1. Under quite general conditions on f(x,y,py′) we show that solution of the singular two point boundary value problem is unique. Here is allowed to have integrable singularity at x=0 and we do not assume . |
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Keywords: | Monotone iterative method Upper and lower solutions Singular boundary value problem Eigenfunction expansion Banach contraction principle Weyl&rsquo s limit circle case |
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