A study of extremal parameter for fractional singular Choquard problem

Abstract

AbstractIn this work, we study the singular problem involving fractional Laplacian operator perturbed with a Choquard nonlinearity using the idea of constrained minimization based on Nehari manifold. Precisely, for some , we have proved the existence of two solutions when the parameter , adding to the existing works dealing with multiplicity of solutions when the parameter λ strictly lies below . We have given a variational characterization of the parametric value , which is an extremal value of the parameter λ involved in the problem up to which the Nehari manifold method can be applied successfully. The paper highlights a fine analysis via fibering maps even for to establish an existence of two different positive solutions for the underlying problem.