Study On The Solutions Of Two Kinds Of Fractional Kirchhoff-Choquard Type Equations

The Kirchhoff-Choquard equation of fractional order has been widely studied in recent years,and the study of the existence of its solution is of great significance.In this paper,the variational method and the concentration-compactness principle are used to study the existence of solutions of two types of fractional Kirchhoff-Choquard type equations.One type is general Kirchhoff-Choquard equation with nonlinearity,and the other is the fractional KirchhoffChoquard equation with power nonlinear terms.In this thesis,we study fractional Kirchhoff-Choquard equations with general nonlinear terms:(?)Thanks to the concentration-compactness principle,the mountain pass lemma,Palais-Smale sequences and new estimates on cut-off function,thus,the existence and non-existent results of non-trivial solutions to the problem was obtained.At the same time,we consider the fractional Kirchhoff-Choquard equation with a power nonlinear term:(?)Using the variational method,the Hardy-Littlewood-Sobolev embedding theorem and the Nehari manifold method,existential results of the non-trivial solution of the problem was obtained.