Global bifurcation from zero in nonlinear Sturm-Liouville equation with a spectral parameter in the boundary condition

Abstract

In this paper, we consider the nonlinear Sturm-Liouville problem with a spectral parameter in the boundary condition. We show the existence of two families of unbounded continua of nontrivial solutions of this problem corresponding to the nodal properties that having the eigenfunctions of the corresponding linear problem and emanating from bifurcation points and intervals of the line of trivial solutions.