MULTIPLICITY OF PERIODIC SOLUTIONS FOR SECOND ORDER HAMILTONIAN SYSTEMS WITH MIXED NONLINEARITIES

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.

Multiple Solutions for p-Laplacian Type Equations

We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form(in particular, a p-Laplacian operator), while the nonlinearity has a(p- 1)-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.

Multiplicity of Homoclinic Solutions for Second Order Hamiltonian Systems with Local Conditions at the Origin

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.

INFINITELY MANY SOLUTIONS TO p(x)-BIHARMONIC PROBLEM WITH NAVIER BOUNDARY CONDITIONS

In this paper, we consider a p（x）-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space.