Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of positive solutions for the equation including singular and nonsingular cases are established. The asymptotic behavior of the solution is also derived, which falls in between two known curves. The interesting points of this paper are that the nonlinearity of the equation may be singular in time and space variables and the corresponding operator can have a singular kernel.

Automated summary

In this paper, the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator is considered. By constructing suitable upper and lower solutions, new results on the existence of positive solutions for the equation, including singular and nonsingular cases, are established. The asymptotic behavior of the solution, which is between two known curves, is also derived. The interesting aspects of this paper are the possible singularity of the nonlinearity in time and space variables and the presence of a singular kernel in the corresponding operator.