具有非对称项p-Laplace方程的无穷多解

Infinitely Many Solutions of p-Laplacian Equations with a Nonsymmetric Term

讨论了有界区域上一类具有非对称扰动项的p-Laplace方程.利用对应的Laplace方程大Morse指标,给出了该问题变分泛函极小极大值序列的一个下界估计,这个估计在一定范围内优于已有的结论.进而得到了无穷多个弱解的存在性.

A class of p-Laplace equation with a nonsymmetric term on a bounded domain is studied. By using the large Morse index of the corresponding Laplace equation, we give a growth estimate about the series of min-max values of associated functional for the problem. The estimate is better than the given result in some range. It is shown that the problem possesses infinitely many weak solutions.