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Positive solutions of singular \(p\)-Laplacian BVPs with sign changing nonlinearity on time scales. (English) Zbl 1156.34309

Summary: We investigate a class of singular \(m\)-point \(p\)-Laplacian boundary value problem on time scales with the sign changing nonlinearity. By using the well-known Schauder fixed point theorem and upper and lower solutions method, some new existence criteria for positive solutions of the boundary value problem are presented. These results are new even for the corresponding differential \((\mathbb T = \mathbb R)\) and difference equations \((\mathbb T=\mathbb Z)\), as well as general time scales setting. As an application, an example is given to illustrate the results.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
39A20 Multiplicative and other generalized difference equations
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