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- W2021567338 abstract "This paper deals with the existence of homoclinic solutions for the following second order non-autonomous Hamiltonian system (HS)q̈+Vq(t,q)=f(t), where V∈C1(R×Rn,R), V(t,q)=−K(t,q)+W(t,q) is T-periodic in t, f is aperiodic and belongs to L2(R,Rn). Under the assumptions that K satisfies the “pinching” condition b1|q|2≤K(t,q)≤b2|q|2, W(t,q) is not globally superquadratic on q and some additionally reasonable assumptions, we give a new existence result to guarantee that (HS) has a homoclinic solution q(t) emanating from 0. The homoclinic solution q(t) is obtained as a limit of 2kT-periodic solutions of a sequence of the second order differential equations and these periodic solutions are obtained by the use of a standard version of the Mountain Pass Theorem. Recent results in the literature are generalized and significantly improved." @default.
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- W2021567338 date "2010-02-01" @default.
- W2021567338 modified "2023-10-16" @default.
- W2021567338 title "Homoclinic solutions for some second order non-autonomous Hamiltonian systems without the globally superquadratic condition" @default.
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- W2021567338 doi "https://doi.org/10.1016/j.na.2009.09.022" @default.
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