nontrivial solution

[数]非平凡解；[数]非无效解

非平凡解，非无效解

colloidal solution───[物化]胶体溶液，胶状溶液

oral solution───口服溶液剂

colloidal solutions───[物化]胶体溶液，胶状溶液

compromise solution───和解解决；折衷解

ideal solution───[化学]理想溶液

oral solutions───口服溶液剂

practical solution───实用的解决方案；切实可行的解决办法

trivialisation───琐碎化

continuing resolution───继续按以前的方案执行

In particular, we use generalized Green's function to prove that the high-order nonhomogeneous boundary value problem has a solution when the associated homogeneous problem has a nontrivial solution.───特别是利用广义格林函数证明了高阶齐次方程存在非平凡解的情况下对应的高阶非齐次边值问题存在一解的充要条件。

The existence of a nontrivial weak solution is established with the help of the first eigenvalue of the corresponding eigenvalue problem, where the eigenvalue parameter is less than a known constant.───相应带不定权特征值问题的第一特征值建立了其非平凡解的存在性定理，其中方程组中特征值参数小于某已知常数。

Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.───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。

1 be fixed, and denote the subset of space such that for any element problem : has a nontrivial solution.───设为定值且表示空间的子集，且对于其中的任一元素问题都有一个非平凡解。

The existence of a nontrivial solution for a semilinear elliptic equation───半线性椭圆型方程非退化解的存在性

Existence of Nontrivial Solution for a Semilinear Elliptic Equation───一类半线性椭圆方程非平凡解的存在性

Nontrivial Solution for A Second-Order Three-Point Boundary Value Problem───一类二阶非线性方程三点边值问题解的存在性

Existence of nontrivial solution for an elliptic equation───一类椭圆型方程的非平凡解的存在性

Nontrivial Solution for a Class of Quasilinear Equation with Natural Growth───一类自然增长的拟线性椭圆型方程的非平凡解