非线性项与特征值相交差的波动方程解的多重性(英文)

Multiplicity of solutions for nonlinear wave equation with nonlinearities crossing eigenvalues

研究了满足Dirichlet 边界条件及周期条件的非线性波动方程解的多重性.应用拓扑度理论,证明了当非线性部分f(u) 与特征值相交差的时候,即当- λ11 < a < - λ00 ,- λ10 < b <- λ21 时,Dirichlet 边界问题至少存在4 个解.

We investigate multiplicity of solutions of the nonlinear wave equation under the Dirichlet boundary condition on the interval (-π/2,π/2) and periodic condition on the variable t .