利用变分法中的三临界点定理,研究一类含参数拟线性椭圆方程组的Dirichlet问题,证明该方程组在其非线项满足某些新的条件时至少存在3个解,并给出该结论在非线性光学中二次谐波产生耦合方程组的一个应用.
Using a three-critical-point theorem in variational methods, we investigated the Dirichlet problem of a class of quasilinear elliptic systems, and proved the existence of at least three weak solutions under some novel assumptions and gave, as the application of the main theorem, an example about the coupling systems come from the second harmonic waves in nonlinear optics.