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We study the periodic and Neumann boundary-value problems associated with the second-order nonlinear differential equation where is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when and λ > 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super–sublinear case