Bifurcation in Singular Self-Adjoint Boundary Value Problems

The bifurcation phenomenon for non-linear perturbations of a class of self-adjoint boundary value problems is studied. In particular, the class includes singular problems of the type (a y')' + by = lambda (y + f(t,y)) m sub 0 y(0) - y' (0) = 0 y epsilon D where D is a Banach space of functions on (0, omega), omega = or < infinity and f is appropriately small for small y. It is shown that if lambda sub 0 is an eigenvalue of the linearized problem (i.e. with f identically equal to 0), there exists a set of solutions, (lambda,y), to the nonlinear problem for lambda near lambda sub 0. (Author)