拉伸扭转不动点定理和非保守变号方程的无穷多周期解的存在性

In this paper, we present and prove a new topological fixed point theorem for the bend-twist map. This theorem can be used to obtain the existence of infinite many periodic solutions for a class of superlinear second order non-conservative equations with indefinite weight. Our arguments are based on the analysis of the qualitative behaviour of the solutions of the equations. In the intervals where the weight is positive, the solutions of the equations have the elastic property and the "strong twist" property. In the intervals where the weight is negative, the superlinearity of $g$ implies a blow-up phenomenon. Then we can prove in some region the Pincare map is well defined. Moreover, it ia a bend-twist map.