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. In this paper, in order to establish the existence criteria for positive solutions of a multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales, first we prove a fixed point theorem on monotone operators and the Ascoli-Arzela’s theorem on time scales. Then using the monotone operator method, we explore the existence criteria of positive solutions for a general multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales with the singular sign-changing nonlinearities and higher-order derivatives. Finally an example is illustrated to indicate the application of our main results, which generalize some well-known results in the literature.

Positive solutions to the singular p-Laplacian BVPs with sign-changing nonlinearities and higher-order derivatives in Banach spaces on time scales