The authors are concerned with the following second-order Neumann boundary value problem:
where is a parameter, (, (, are continuous functions with and . Under some assumptions regarding the limits , the authors first prove the existence of single and twin positive solutions. They use Krasnosel’skii’s fixed point theorem of cone compression and expansion both with a fixed point theorem for strongly completely continuous mappings; a discussion upon the parameter is given and a nonexistence result presented. When the nonlinearity further satisfies a monotonicity condition, a uniqueness result is obtained together with the continuous dependence of the solutions on .