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。
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.
借助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。
A class of nonlinear delay difference equations is considered. The non-convergence of nontrivial positive solution of the equations is proved by direct computation method.
考虑一类非线性时滞差分方程，用直接计算的方法，证明了它的所有非平凡正解都是发散的。
Further, the existence of a nontrivial periodic solution is considered by using bifurcation theory.
利用分支理论分析了非平凡周期解的存在性。
The non-convergence of nontrivial positive solution of the equations is proved by direct computation method.
考虑一类非线性时滞差分方程，用直接计算的方法，证明了它的所有非平凡正解都是发散。
The non-convergence of nontrivial positive solution of the equations is proved by direct computation method.
考虑一类非线性时滞差分方程，用直接计算的方法，证明了它的所有非平凡正解都是发散。
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