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Multiplicity of periodic orbits for a class of second order Hamiltonian systems with superlinear and sublinear nonlinearity

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  • Cheng, Bitao

Abstract

This paper is concerned with a class of second order Hamiltonian systems with superlinear and sublinear nonlinearity(P)u¨(t)+b(t)|u(t)|μ-2u(t)+∇H(t,u(t))=0,a.e.t∈[0,T];u(0)-u(T)=u˙(0)-u˙(T)=0,where b(t) is a real function defined on [0,T], μ>2 and H : [0,T]×RN→R is a Carathéodory function. Some new multiplicity results of periodic orbits for the problem (P) are obtained via some critical point theorems.

Suggested Citation

  • Cheng, Bitao, 2011. "Multiplicity of periodic orbits for a class of second order Hamiltonian systems with superlinear and sublinear nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 811-816.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:811-816
    DOI: 10.1016/j.chaos.2011.06.005
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