Study On Ground State Solutions Of Two Classes Of Fractional Laplace Equations With Logarithmic Terms

With the rapid development of financial mathematics,fluid dynamics,mechanics of materials,quantum mechanics and other fields,more and more complex mathematical models make many researchers focus on the study of fractional Laplace equation,in which the existence of weak solutions is an attractive research direction.In recent years,many scholars have also studied the existence of solutions to partial differential equations with logarithmic nonlinear terms.Inspired by relevant research work,this paper first generalizes the general fractional logarithmic Sobolev inequalities and obtain two more general fractional logarithmic Sobolev inequalities.Then,the existence of solutions for two kinds of fractional Laplace equation with logarithmic nonlinear terms is discussed by applying Linking theorem,and the existence of ground state solutions is obtained.