Multiple Positive Solutions for Fractional Schrodinger-Poisson System with Doubly Critical Exponents

In this article, we study the following fractional Schrodinger-Poisson system {(-delta)(s)u + V(x)u - ?|u|(2)(s)*-3u = |u|(2)(s)*-2u + lambda f(x), x is an element of R-3, (-delta)(s)? = |u|(2)(s)*-1, x is an element of R-3, where s is an element of (0, 1), 2(s)* = 6/3-2s, lambda > 0 is a real parameter, f and V satisfy some suitable hypothesis. Via applying the variational methods and mountain pass theorem, we prove that there exists lambda* > 0 such that the system has at least two positive solutions for any lambda is an element of (0, lambda*) which supplements and generalizes the previous results in the literature.

Automated summary

In this article, the authors study the fractional Schrodinger-Poisson system and prove the existence of lambda* > 0 such that the system has at least two positive solutions for any lambda in the range (0, lambda*), using variational methods and the mountain pass theorem. This result supplements and generalizes previous findings in the literature.