EXISTENCE OF SOLUTIONS FOR SOME SINGULAR HIGHER-ORDER BOUNDARY-VALUE-PROBLEMS

Solutions are obtained for the boundary value problem, y(n) + psi(x) f(x,y,y',...,y(n-1)) = 0, y(i)(0) = 0, 0 less-than-or-equal-to i less-than-or-equal-to k - 1, and y(j)(1) = 0, k less-than-or-equal-to i less-than-or-equal-to n - 1, where psi(x) is singular at x = 0,1, and f(x,y1,...,y(n)) is singular at y(i) = 0, 1 less-than-or-equal-to i less-than-or-equal-to n. The techniques involve topological transversality methods.