The concentration behavior of ground state solutions for a fractional Schrodinger-Poisson system

作者：Yu, Yuanyang; Zhao, Fukun^*; Zhao, Leiga

来源：Calculus of Variations and Partial Differential Equations, 2017, 56(4): 116.

DOI：10.1007/s00526-017-1199-4

• POSITIVE BOUND-STATES
• SEMICLASSICAL LIMITS
• STANDING WAVES
• EQUATION
• REGULARITY

In this paper, we study the following fractional Schrodinger-Poisson system @@@ {epsilon(2s) (-Delta)(s) u + V (x) u + phi u = K (x) |u|(p-2) u, in R-3, @@@ epsilon(2s) (-Delta)(s) phi = u(2), in R-3, (0.1) @@@ where epsilon > 0 is a small parameter, 3/4 < s < 1, 4 < p < 2*(s) := 6/3-2s, V (x) is an element of C (R-3) boolean AND L-infinity (R-3) has positive global minimum, and K (x) is an element of C (R-3) boolean AND L-infinity (R-3) is positive and has global maximum. We prove the existence of a positive ground state solution by using variational methods for each epsilon > 0 sufficiently small, and we determine a concrete set related to the potentials V and K as the concentration position of these ground state solutions as epsilon -> 0. Moreover, weconsidered some properties of these ground state solutions, such as convergence and decay estimate.

• 出版日期2017-8
• 单位云南师范大学; 北京化工大学