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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.
We study the existence of positive solutions for equations of the form
where 0 < ω < π, subject to various non-local boundary conditions defined in terms of the Riemann–Stieltjes integrals. We prove the existence and multiplicity of positive solutions for these boundary value problems in both resonant and non-resonant cases. We discuss the resonant case by making a shift and considering an equivalent non-resonant problem.
