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

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 - 2 u ( 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] × R N → R is a Carathéodory function. Some new multiplicity results of periodic orbits for the problem ( P) are obtained via some critical point theorems.