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Infinitely Many Solutions for Fractional Hamiltonian Systems with Locally Defined Potentials |
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PP: 231-240 |
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doi:10.18576/pfda/100204
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Author(s) |
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Wafa Selmi,
Mohsen Timoumi,
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Abstract |
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| Abstract: In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian
where −∞ Dtα and t Dα∞ are left and right Liouville-Weyl fractional derivatives of order 1 < α < 1 on the whole axis respectively, 2
L ∈C(R,RN2) is a symmetric matrix valued function unnecessary coercive and W(t,x) ∈C1(R×RN,R). The novelty of this paper is that, assuming that L is bounded from below and unnecessarily coercive at infinity, and W is only locally defined near the origin with respect to the second variable, we show that (1) possesses infinitely many solutions via a variant Symmetric Mountain Pass Theorem.
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