An elliptic problem involving critical Choquard and singular discontinuous nonlinearity

The present article investigates the existence, multiplicity and regularity of weak solutions of problem involving a combination of critical Hartree-type nonlinearity along with singular and discontinuous nonlinearities (see ( P (lambda) ) below). By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of lambda and gamma. Finally by studying the L-infinity-estimates and boundary behaviour of weak solutions, we prove their H & ouml;lder and Sobolev regularity.