On a class of regular singular two point boundary value problems

[摘要] Existence of a unique solution for a class of regular singular two point boundary value problems -(p(x)y')' = p(x)f(x,y), 0 < x less than or equal to b, (x --> 0+)lim y'(x) = 0, y(b) = B, has been established where p(x) satisfies (i) p(x) > 0 on (0, b), (ii) p(x) is an element of C-1(0, r), and for some r > b, (iii) xp'(x)/p(x) is analytic in {z:\z\ < r} with Taylor expansion xp'(x)/p(x) = b(0) + b(1)x + ..., b(0) greater than or equal to 1 and with quite general conditions on f(x,y). These conditions on f(x,y) are sharp, which is seen through one example. Regions for multiple solutions have also been determined. (C) 1997 Academic Press.

[发布日期] 1997-04-15