A necessary and sufficient condition for the existence of entire large solutions to a k-Hessian system

A Singular Tempered Sub-Diffusion Fractional Equation with Changing-Sign Perturbation

“…However, there are no results for sub-diffusion model with a changing-sign perturbation even for the perturbation which is only a time-variable function without a lower-order sub-diffusion term. This is mainly because many nonlinear analysis theories and methods, such as the spaces theories [40][41][42][43][44], smooth theories [45][46][47], operator method [48,49], the method of moving sphere [50], critical point theories [51][52][53][54] and iterative techniques [55][56][57], have not been used to solve the sub-diffusion model when the main nonlinear term f and the changing-sign perturbation g all involve a lower-order tempered fractional sub-diffusion term. In the present paper, by using the spaces theories, regularity theories, operator theories and the technique of moving plane, we firstly transform the changing-sign subdiffusion model to a positive problem and then derive sufficient conditions on the existence of positive solutions of the changing-sign sub-diffusion model (3) based on the fixed-point theorem in the cone.…”