Multiplicity of Positive Solutions for a Singular Tempered Fractional Initial-Boundary Value Problem with Changing-Sign Perturbation Term

In this paper, we focus on the multiplicity of positive solutions for a singular tempered fractional initial-boundary value problem with a p-Laplacian operator and a changing-sign perturbation term. By introducing a truncation function and combing with the properties of the solution of isomorphic linear equations, we transform the changing-sign tempered fractional initial-boundary value problem into a positive problem, and then the existence results of multiple positive solutions are established by the fixed point theorem in a cone. It is worth noting that the changing-sign perturbation term only satisfies the weaker Carathèodory conditions, which implies that the perturbation term ℏ can be allowed to have an infinite number of singular points; moreover, the value of the changing-sign perturbation term can tend to negative infinity in some singular points.