4 papers
Existence and uniqueness of solutions to Liouville equation
Alireza Ataei
We prove some general results on the existence and uniqueness of solutions to the Liouville equation. Then, we discuss the sharpness and possible generalizations. Finally, we give…
Existence and uniqueness of the solutions to convection-diffusion equations
Alireza Ataei
In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove…
A comparison method for the fractional Laplacian and applications
Alireza Ataei, Alireza Tavakoli
We study the boundary behavior of solutions to fractional elliptic equations. As the first result, the isolation of the first eigenvalue of the fractional Lane-Emden equation is pr…
Applications of a theorem by Ky Fan in the theory of weighted Laplacian graph energy
Reza Sharafdini, Alireza Ataei, Habibeh Panahbar
The energy of a graph is equal to the sum of the absolute values of the eigenvalues of , which in turn is equal to the sum of the singular values of the adjacency matrix of…