A comparison of two methods on non-uniqueness for a class of two-point boundary value problems

Abstract

We consider two methods that have been used in [1] to prove multiple non-negative solutions for nonlinear boundary value problems of the form-u′(x) =λf(u(x)) ; x ϵ (0,1)u(0) = 0 =u(1) ,namely (A) using a quadrature technique and (B) using sub-super solutions. In this short paper we compare these methods and give an interesting proof showing that (A) is often sharper than (B) for establishing non-uniqueness. However, we also point out the advantage of (B) over (A)