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.
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。
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.
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。
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.
在适当的条件下，通过建立一个先验不等式，证明了其唯一非负解是平凡的。
By establishing a prior inequality, we prove that, under suitable conditions, the unique non-negative solutions of the problems are trivial.
利用分支理论分析了非平凡周期解的存在性。
Further, the existence of a nontrivial periodic solution is considered by using bifurcation theory.
运用分歧理论，隐函数定理，以及渐近展开的方法，获得了非平凡周期解的存在性。
The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.
这个结果导致捕食食饵系统的持久性、平凡解和所有半平凡解的不稳定性和不存在非一致平衡解。
The result leads to the permanence of the prey-predator systems, the instability of the trivial and all forms of semitrivial solutions, and the nonexistence of nonuniform steady-state solutions.
获得了解的整体存在惟一性，并给出了非平凡平衡解局部渐近稳定性易验证的充分条件。
The global existence-uniqueness of solutions is obtained and the easy verifiable sufficient conditions for local asymptotic stability of a non-trivial steady-state solutions are given.
获得了解的整体存在惟一性，并给出了非平凡平衡解局部渐近稳定性易验证的充分条件。
The global existence-uniqueness of solutions is obtained and the easy verifiable sufficient conditions for local asymptotic stability of a non-trivial steady-state solutions are given.
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