Abstract
We shall present a new version of a recently appeared theorem for the existence and localization of solutions of the Neumann problem associated to the equation $ -u^{\prime\prime} + u = \beta(t)g(u) $ , based on a general variational principle by Ricceri. Our study will be especially aimed to express a certain hypothesis regarding the function g in its sharpest form, and a ‘limit case’ is enquired by an approximation
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