Journal
ACTA MATHEMATICA SCIENTIA
Volume 40, Issue 4, Pages 1064-1080Publisher
SPRINGER
DOI: 10.1007/s10473-020-0413-1
Keywords
fractional Schrodinger-Poisson system; Nehari-Pohozaev manifold; ground state solutions; critical growth
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Funding
- Science and Technology Project of Education Department in Jiangxi Province [GJJ180357]
- NSFC [11701178]
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We study the following nonlinear fractional Schrodinger-Poisson system with critical growth: {(-Delta)(s)u + u + phi u = f(u) + vertical bar u vertical bar(2)*(s-2) u, x is an element of R-3, (-Delta)(t)phi = u(2), x is an element of R-3, (0.1) where 0 < s, t < 1, 2s + 2t > 3 and 2(s)* = 6 3-2s is the critical Sobolev exponent in R-3. Under some more general assumptions on f, we prove that (0.1) admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.
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