On solvability of derivative dependent doubly singular boundary value problems |
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Authors: | R K Pandey Amit K Verma |
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Institution: | 1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India
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Abstract: | In this paper we establish existence of solutions of singular boundary value problem ?(p(x)y ′(x))′=q(x)f(x,y,py′) for 0<x≤b and $\lim_{x\rightarrow0^{+}}p(x)y^{\prime}(x)=0$ , α 1 y(b)+β 1 p(b)y ′(b)=γ 1 with p(0)=0 and q(x) is allowed to have integrable discontinuity at x=0. So the problem may be doubly singular. Here we consider $\lim_{x\rightarrow0^{+}}\frac{q(x)}{p'(x)}\neq0$ therefore $\lim_{x\rightarrow0^{+}}p(x)y'(x)=0$ does not imply y′(0)=0 unless $\lim_{x\rightarrow0^{+}}f(x,y(x),p(x)y'(x))=0$ . |
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