Positive Solutions for Singular Third-Order Boundary Value Problem with Dependence on the First Order Derivative on the Half-Line

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By using fixed-point index theory and a new fixed-point theorem in cones, some sufficient conditions for the existence of countably many positive solutions for singular third-order boundary value problem on the half-line are established, which are the complement of previously known results. The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative u′.