Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities

Abstract: In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem also includes a Hardy-type term; additionaly, all terms have critical singular weights. Our result improve upon previous work in the following ways: we focus our attention on the existence of a nontrivial weak solution for fractional p-Kirchhoff equation in the entire space R^N. The possibility of a slower growth in the nonlinearity makes it more difficult to establish a compactness condition; to do so, we use the Cerami condition. The crucial points in our argument are the uniform boundedness of the convolution part and the lack of compactness of the Sobolev embeddings.