BOUND STATES FOR FRACTIONAL SCHRODINGER-POISSON SYSTEM WITH CRITICAL EXPONENT

摘要

This paper deals with the fractional Schrodinger-Poisson system @@@ {epsilon(2s) (-Delta)(s)u + V(x)u + K(x)phi u = vertical bar u vertical bar(2s)*(-2)u, in R-3, (-Delta)(t) phi = K(x)u(2), in R-3, @@@ where s is an element of (3/4, 1), t is an element of (0; 1), is an element of is a positive parameter, 2(s)* = 6/3-2s is the critical Sobolev exponent. K(x) is an element of 6/L2t+4s-3 (R-3), V(x) is an element of 3/L-2s (R-3) and V(x) is assumed to be zero in some region of R-3, which means that the problem is of the critical frequency case. In virtue of a global compactness result in fractional Sobolev space and Lusternik-Schnirelman theory of critical points, we succeed in proving the multiplicity of bound states.

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