A class of second order non-autonomous Hamiltonian systems with asymptotically quadratic conditions is considered in this paper.Using Fountain Theorem,one multiplicity result of periodic solutions is obtained,which improves some previous results.
The multiplicity of periodic solutions for a class of second order Hamiltonian system with superquadratic plus subquadratic nonlinearity is studied in this paper.Obtained via the Symmetric Mountain Pass Lemma,two results about infinitely many periodic solutions of the systems extend some previously known results.
By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.
In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systemsü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L∈C(R,RN×N)is symmetric but non-periodic,W∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.
