EXISTENCE OF POSITIVE SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL EQUATION AT RESONANCE

摘要

We establish sufficient conditions for the existence of positive solutions to the multipoint boundary value -u" = f(t,u(t)), t∈(0,1), u(0) = u(1), u'(0) =u'(η). Since the associated homogeneous boundary value problem is not invertible the problem is said to be at resonance. The main tool employed is a variant of a fixed point index theorem due to Cremins for A-proper semilinear operators defined on cones.