一类非线性波动方程解的多重性

Multiplicity Results for a Nonlinear Wave Equation with Nonlinearities Crossing Eigenvalues

主要考察了在狄利克莱边界条件下的一类非线性波动方程.利用变分方法理论,把无限维的问题转化为有限维的问题,讨论了当方程的非线性项介于特征值之间时,方程的外部项与方程解的多重性之间的关系.

The multiplicity results for a nonlinear wave equation under Dirichlet boundary condition are studied. By using the variational reduction method, the problem from an infinite dimensional one to a finite one is reduced, and the relationships between multiplicity of solution and source terms in equation when nonlinearities crossing eigenvalues are revealed.