Positive solution for a boundary singular semilinear equation with Hardy–Sobolev exponent

ABSTRACT

In this paper, we establish the existence of at least one positive solution to a singular elliptic equation with zero boundary data and critical Hardy–Sobolev exponent. We show that the existence of the positive solution in high dimension depends on the sign of the mean curvature of the boundary near zero and in the low dimensions, it depends on the mass of the domain.

Keywords:

• Semilinear elliptic equation
• critical Hardy–Sobolev exponent
• boundary singularities
• Hardy–Schrödinger operator

AMS Subject Classifications:

• 35J10
• 35J20
• 35J25
• 35J66
• 35J75

View correction statement:

Correction

Acknowledgments

I would like to thank Prof. Frederic Robert for welcoming me to ”L'institue Élie Cartan de Lorraine” and for his help and availability.

Disclosure statement

No potential conflict of interest was reported by the author(s).