Existence of solutions to fractional Hamiltonian systems with combined nonlinearities
| dc.contributor.author | Zhang, Ziheng | |
| dc.contributor.author | Yuan, Rong | |
| dc.date.accessioned | 2023-06-12T17:25:12Z | |
| dc.date.available | 2023-06-12T17:25:12Z | |
| dc.date.issued | 2016-01-27 | |
| dc.description.abstract | This article concerns the existence of solutions for the fractional Hamiltonian system -tDα∞(-∞Dtαu(t)) - L(t)u(t) + ∇W(t, u(t)) = 0, u ∈ Hα(ℝ, Rn), where α ∈ (1/2, 1), L ∈ C(ℝ, ℝn2) is a symmetric and positive definite matrix. The novelty of this article is that if τ1|u|2 ≤ (L(t)u, u) ≤ τ2|u|2 and the non-linearity W(t, u) involves a combination of superquadratic and subquadratic terms, the Hamiltonian system possesses at least two nontrivial solutions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Zhang, Z., & Yuan, R. (2016). Existence of solutions to fractional Hamiltonian systems with combined nonlinearities. Electronic Journal of Differential Equations, 2016(40), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16914 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Hamiltonian systems | |
| dc.subject | Critical point | |
| dc.subject | Variational methods | |
| dc.subject | Mountain pass theorem | |
| dc.title | Existence of solutions to fractional Hamiltonian systems with combined nonlinearities | |
| dc.type | Article |