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Existence of solutions for first-order multi-point problems with changing-sign nonlinearity

In this study, conditions for the existence of at least one positive solution to a nonlinear first-order multi-point eigenvalue problem on time scales are discussed. Here the nonlinearity is allowed to take on negative values. The results, which are new for differential/difference equations as well as arbitrary time scales, are based on the Guo–Krasnosel'skii fixed point theorem.