Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign
The paper deals with the existence of periodic solutions of the system (1) \(\ddot x + b(t) V'(x(t)) = 0\) where \(b(t)\) is a continuous \(T\)- periodic \((T > 0)\) real function and \(V\) has a superquadratic behavior. In case that \(b(t)\) changes its sign, some results have been obtained in other papers but under the assumption that \(V\) is homogeneous. Here the case \(\int^ T_ 0 b(t)dt \neq 0\) is considered and the homogeneity assumption on \(V\) is weakened, in the sense that one requires that \(V\) differs from a homogeneous superquadratic function by a quadratic term, outside a sufficiently large sphere. Several theorems which discuss the existence of periodic solutions of equation (1) are proved.
scientific article; zbMATH DE number 736849