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

This paper is concerned with a class of second order Hamiltonian systems with superlinear and sublinear nonlinearityequation(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.

► We study a class of second order Hamiltonian systems with superlinear and sublinear nonlinearity.
► Some new solvable conditions of periodic orbits for the system are established.
► Some new multiplicity results of periodic orbits for the system are obtained via some critical point theorems.
► The methods and results are different from the past references.