Positive solutions for nonlinear Choquard equation with singular nonlinearity

Abstract

In this article, we study the following non-linear Choquard equation with singular non-linearity

where is a bounded domain in with smooth boundary , and . Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positive weak solutions of the above problem, if is less than some positive constant. We also study the regularity of these weak solutions.

Keywords:

• Choquard equation
• Nehari manifold
• singular non-linearity

AMS Subject Classifications:

• 35R11
• 35R09
• 35A15

Notes

No potential conflict of interest was reported by the authors.