Existence of positive solutions for a class of critical fractional Schrödinger–Poisson system with potential vanishing at infinity

An improved result for a class of Klein–Gordon–Maxwell system with quasicritical potential vanishing at infinity

“…A nontrivial positive solution for a Schrödinger-Poisson system with a radial potential vanishing at infinity was got by Sun et al in [17]. Furthermore, a positive solution for a class of critical fractional Schrödinger-Poisson system with potential vanishing at infinity was got by Gu et al in [12]. When 𝑓(𝑢) = |𝑢| 𝑞−2 𝑢 and 𝑉 is a zero mass potential, Chen and Li in [8] investigated infinitely many solutions for problem (1.1).…”

“…in [17]. Furthermore, a positive solution for a class of critical fractional Schrödinger–Poisson system with potential vanishing at infinity was got by Gu et al in [12]. When $$f(u)=|u|^{q-2}u$$ and V is a zero mass potential, Chen and Li in [8] investigated infinitely many solutions for problem (1.1).…”

Existence and Symmetry of Solutions for a Class of Fractional Schrödinger–Poisson Systems

“…For example, Azzollini and Pomponio in [15] considered system (3) by variational methods; they established the existence of a ground state solution when potential V(x) is a positive constant or non-constant. Fractional Schrödinger-Poisson systems have received lots of attention in recent years, and many of the works have studied the existence of solutions of it; see [18][19][20][21][22] and their references. As far as we know, few studies have considered the existence of solutions for the fractional Schrödinger-Poisson system with critical growth.…”

“…As far as we know, few studies have considered the existence of solutions for the fractional Schrödinger-Poisson system with critical growth. Gu et al in [19] only studied the existence of a positive solution by variational methods, and there are no relevant articles that consider the existence of radially symmetric solutions of the fractional Schrödinger-Poisson system with critical growth. We tried to deal with this problem and obtained novel existence results by using new analytical methods, which are different from the related conclusions on this topic.…”

Fractional Schrödinger–poisson System With Singularity: Existence, Uniqueness, and Asymptotic Behavior

“…Under some hypotheses, He and Jing [16] showed the existence and multiplicity of nontrivial solutions for system (1.1) by replacing λ with a suitable function K(x). Gu et al [14] showed the existence of positive solutions for system (1.1) with [29,34] obtained the existence of a positive (nontrivial) ground state solution and a sign-changing (least energy) solution for system (1.1) involving critical nonlinearities. Xiang and Wang [33] considered the existence, multiplicity, and asymptotic behavior of nonnegative solutions for a fractional Schrödinger-Poisson-Kirchhoff type system involving critical nonlinearities.…”