Non-trivial solutions of fractional Schrödinger-Poisson systems with sum of periodic and vanishing potentials
| dc.contributor.author | Yu, Mingzhu | |
| dc.contributor.author | Chen, Haibo | |
| dc.date.accessioned | 2021-12-03T15:35:03Z | |
| dc.date.available | 2021-12-03T15:35:03Z | |
| dc.date.issued | 2019-09-04 | |
| dc.description.abstract | We consider the fractional Schrödinger-Poisson system (-Δ)αu + V(x)u + K(x)Φ(x)u = ƒ(x, u) - Γ(x)|u|q-2u in ℝ3, (-Δ)βΦ = K(x)u2 in ℝ3, where α, β ∈ (0, 1], 4α + 2β > 3, 4 ≤ q < 2*α, K(x), Γ(x) and ƒ(x, u) are periodic in x, V is coercive or V = Vper + Vloc is a sum of a periodic potential Vper and a localized potential Vloc. If ƒ has the subcritical growth, but higher than Γ(x)|u|q-2u, we establish the existence and nonexistence of ground state solutions are dependent on the sign of Vloc. Moreover, we prove that such a problem admits infinitely many pairs of geometrically distinct solutions provided that V is periodic and ƒ is odd in u. Finally, we investigate the existence of ground state solutions in the case of coercive potential V. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Yu, M., & Chen, H. (2019). Non-trivial solutions of fractional Schrödinger-Poisson systems with sum of periodic and vanishing potentials. <i>Electronic Journal of Differential Equations, 2019</i>(102), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14994 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Schrödinger-Poisson system | |
| dc.subject | Coercive potential | |
| dc.subject | Periodic and localized potential | |
| dc.subject | Nehari manifold | |
| dc.subject | Variational method | |
| dc.title | Non-trivial solutions of fractional Schrödinger-Poisson systems with sum of periodic and vanishing potentials | en_US |
| dc.type | Article |