Positive solutions of elliptic equations with a strong singular potential

Abstract

In this paper, we study positive solutions of the elliptic equationis often called a Hardy potential, and the equation in this case has been extensively investigated. Here we consider the case α > 2, which gives a stronger singularity than the Hardy potential near ∂Ω. We show that when λ < 0, the equation has no positive solution, while when λ > 0, the equation has a unique positive solution, and it satisfies

On the existence of solutions for a multi-singular pointwise defined fractional system

“…It is natural that many phenomena could be modeled by using singular fractional integro-differential equations. Due to the emergence of fractional differential equations in some mathematical models of distinct phenomena in the world, fractional calculus is perfectly appealing ( [1][2][3][4][5][6][7][8][9][10][11][12]) for some real modelings ( [13][14][15]). On the other side, much work is conducted in the field of fractional differential equations among which some have a singular point to control these sorts of points ( [16][17][18][19]) and we have nonlinear delay-fractional differential equations ( [20][21][22][23]).…”