Nodal solutions for singular nonlinear eigenvalue problems

We are concerned with determining values of r , for which there exist nodal solutions of the boundary value problems u ″ + r a ( t ) f ( u ) = 0 , 0 t 1 , u ( 0 ) = u ( 1 ) = 0 where r is a parameter, and a : ( 0 , 1 ) → [ 0 , ∞ ) is continuous and satisfies 0 ∫ 0 1 t ( 1 − t ) a ( t ) d t ∞ . The proof of our main result is based on bifurcation techniques.