On a Class of Weakly Regular Singular Two-Point Boundary Value Problems, II

Abstract

Existence of a unique solution of a class of weakly regular singular two point boundary value problems −(p(x)y′)′=p(x)f(x, y), 0<x⩽b, limx→0+y′(x)=0,y(b)=B, has been established, wherep(x) satisfies: (i) p(x)>0 on (0, b); (ii) p(x)∈C1(0, r), and for somer>b; (iii) xp′(x)/p(x) is analytic in {z:|z|<r} with Taylor expansionxp′(x)/p(x)=b0+b1x+…b0∈[0, 1) and with quite general conditions onf(x, y). These conditions onf(x, y) are sharp, which is seen through one example. Regions for multiple solutions have also been determined.