Bound state solutions for some non-autonomous asymptotically cubic Schrödinger–Poisson systems

Existence and concentration of solution for Schrödinger-Poisson system with local potential

“…If the potential is radial symmetry and has asymptotical behavior at infinity, Li et al [23] studied the existence of infinitely many sign-changing solutions. For other related nonlocal variational problems, We refer the interested readers to see [3,10,16,24,28,29,33] and the references therein.…”

Existence of Ground State Solutions for a Class of Non-Autonomous Fractional Kirchhoff Equations

“…dx (−∆) s u + u = K(x)|u + | 3 , in R 3 (29). By using u − as a test function in(29) we obtain0 = 1 + b R dx ≥ 0,which yields that u − = 0, and hence, u ≥ 0. Furthermore, if u(x 0 ) = 0 for some x 0 ∈ R 3 , then (−∆) s u(x 0 ) = 0.…”

“…The authors in [28] produced a result for the Schrödinger-Poisson system that was comparable. For further results involving the aforementioned comparable conditions, see [29][30][31], and references therein. To the best of our knowledge, it appears that no studies have been performed regarding the existence of the ground state solution of (1).…”

“…In order to find a way around this problem, we took a hint from [32], where they discovered that the quasilinear Schrödinger equation with three times growth has infinitely many geometrically distinctive solutions. For a few related papers, see [29,33], along with the citations therein.…”