非平凡解是矩阵代数中的定义，属高等数学内容。非平凡解是齐次方程或齐次方程组的非零解。
借助特征值法，研究相应弹性变形非平凡解的P-稳定性。
With the aid of eigenvalue, the P-stability of some non-trivial solutions of the mathematical model is achieved.
最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。
Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.
本文讨论一类变系数带临界指数的椭圆型方程，主要考虑上述问题的非平凡解的存在性，包括多解与非存在性。
In this paper, we study the existence of multiple nontrivial solutions for the variable coefficient elliptic equations with critical Sobolev exponents.
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