Existence Of Sign-changing Solutions For Some Fractional Elliptic Equations

In this paper,we study some fractional elliptic equations.The existence and convergence property of solution are established.Our method relies upon variational principle and some analysis techniques.First,we consider the following fractional Schr(?)dinger-Poisson system with critical nonlinearity and subcritical perturbation:(?)where ?>0,q ?(1,2s*-1),2s*=6/3-2s is the fractional Sobolev critical exponent,s,t?(0,1)and 2s+2t>3,(-?)s is the fractional Laplace operator defined by the Cauchy principal value integral(?).With the help of sign-changing Nehari manifold,we obtain that the system has a ground state sign-changing solution under some suitable conditions on V(x).And then we study the following fractional Kirchhoff-Schr(?)dinger-Poisson sys-tem with general nonlinearity:(?)where a,b>0,s,t ?(0,1),(-?)s and(-?)t also stand for the fractional Laplacian operators defined by the Cauchy principal value integral.We impose the following conditions on V(x).With the help of sign-changing Nehari manifold and quantita-tive deformation lemma,we obtain that the system has a ground state sign-changing solution,which changes sign only once under some suitable conditions on V(x),f(x,u).Moreover,we give a convergence property of solution as b?0.