Resumen de Ground State Sign-Changing Solution for a Fractional Schrödinger-Poisson System with Critical Exponent and Steep Potential Well
Jiao Fu, Jia Feng Liao
In this paper, we consider the following fractional Schrödinger-Poisson system with critical exponent (−)su + Vλ(x)u + φu = |u| 2∗ s −2u + f (u), in R3, (−)t φ = u2, in R3, where s ∈ ( 3 4 , 1), t ∈ (0, 1), 2∗ s := 6 3−2s is the fractional critical exponent, Vλ(x) = λV(x)+1 with λ > 0. Under some suitable assumptions on f and V, if λ > 0 is large enough, we prove the existence of ground state sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma. Moreover, the least energy of sign-changing solution is strictly more than twice the energy of the ground state solution. At the same time, we also study the asymptotic behavior of ground state sign-changing solutions as λ → ∞. Our results improve the recent results in the literature.
