Qualitative properties and global bifurcation ofsolutions for a singular boundary value problem

摘要

This paper deals with a singular, nonlinear Sturm–Liouville problem of theform {A(x)u0(x)}0 + λu(x) = f(x, u(x), u0(x)) on (0, 1) where A is positive on (0, 1] butdecays quadratically to zero as x approaches zero. This is the lowest level of degeneracyfor which the problem exhibits behaviour radically different from the regular case. Inthis paper earlier results on the existence of bifurcation points are extended to yieldglobal information about connected components of solutions.