| 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 μ>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. |
