Solutions for perturbed fractional Hamiltonian systems without coercive conditions View Full Text


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Article Info

DATE

2015-12

AUTHORS

Xionghua Wu, Ziheng Zhang

ABSTRACT

In this paper we are concerned with the existence of solutions for the following perturbed fractional Hamiltonian systems: −tD∞α(−∞Dtαu(t))−L(t)u(t)+∇W(t,u(t))=f(t), u∈Hα(R,Rn) (PFHS), where α∈(1/2,1), t∈R, u∈Rn, L∈C(R,Rn2) is a symmetric and positive definite matrix for all t∈R, W∈C1(R×Rn,R), and ∇W(t,u) is the gradient of W(t,u) at u, f∈C(R,Rn) and belongs to L2(R,Rn). The novelty of this paper is that, assuming L(t) is bounded in the sense that there are constants 0<τ1<τ2<∞ such that τ1|u|2≤(L(t)u,u)≤τ2|u|2 for all (t,u)∈R×Rn and W(t,u) satisfies the Ambrosetti-Rabinowitz condition and some other reasonable hypotheses, f(t) is sufficiently small in L2(R,Rn), we show that (PFHS) possesses at least two nontrivial solutions. Recent results are generalized and significantly improved. More... »

PAGES

149

References to SciGraph publications

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http://scigraph.springernature.com/pub.10.1186/s13661-015-0406-5

DOI

http://dx.doi.org/10.1186/s13661-015-0406-5

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https://app.dimensions.ai/details/publication/pub.1018947230


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