GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS

Ying Lv; Chunlei Tang; Boling Guo

doi:10.11948/2018.620

2018 Volume 8 Issue 2

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Ying Lv, Chunlei Tang, Boling Guo. GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 620-648. doi: 10.11948/2018.620

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Ying Lv, Chunlei Tang, Boling Guo. GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 620-648. doi: 10.11948/2018.620

GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS

1 School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2 Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

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Abstract

Abstract

In this paper, we consider a class of Hamiltonian systems of the form _tD_∞^α (-_∞D_tαu(t)) + L(t)u(t) -∇W (t,u(t))=0 where α ∈ (1/2,1), -_∞D_t^α and _tD_∞^α are left and right Liouville-Weyl fractional derivatives of order α on the whole axis R respectively. Under weaker superquadratic conditions on the nonlinearity and asymptotically periodic assumptions, ground state solution is obtained by mainly using Local Mountain Pass Theorem, ConcentrationCompactness Principle and a new form of Lions Lemma respect to fractional differential equations.
- Fractional Hamiltonian systems /
- ground state /
- local mountain pass theorem /
- concentration-compactness principle
MSC: 34C37;58E05;70H05

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References

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