1) trivial solution
平凡解
1.
It is also demonstrated that the solution must be trivial solution if the solution vanishes at the parabolic boundary of Q.
在空间E~(n+1)的区域Q=Ω×(O,T)考虑满足较一般结构条件的一类退缩抛物型方程(1),证明广义解的有界性,以及如果它的解在Q的抛物边界等于零时,必是平凡解。
2.
It is proved that the global solution for the homogeneous Cauchy problen of a class degenerate parabolic equation, u, is only a trivial solution provided there exists a proper a>o such that u ∈ Lu (En×(0,∞)
本文证明下面的抛物型方程(1)的齐次Cauchy问题的整体解u只能是平凡解,如果存在适当a>0,使u∈L_a(E~n×(0,∞))。
2) semi-trivial solutions
半平凡解
1.
The sufficient conditions for the existence of the local bifurcations of two semi-trivial solutions(θr,0) and(0,θd) are proved,and stability of the local bifurcate solution from semi-trivial solution(θr,0) is obtained.
利用局部分歧理论及线性稳定理论,证明了两个半平凡解(rθ,0)和(0,θd)局部分歧解存在的充分条件,并且证明了半平凡解(rθ,0)产生的局部分歧解是无条件稳定的。
3) nontrivial solutions
非平凡解
1.
We obtained that for every λ>0 in the minimum problems Iλ and I∞λ,there exists α∈0,λ,such that both problems Iα and I∞α have nontrivial solutions.
讨论了一类拟线性椭圆型方程的CHOQUARD-PEKAR问题在无界区域中的非平凡解的存在性,对于极小问题Iλ和I∞λ,得到了对于每个λ>0,存在α∈(0,λ],使得Iα和I∞α可以达到。
2.
In this paper, a concentration-compactness lemma for the problem of quasilinear elliptic equations is given, and the existence of nontrivial solutions is discussed by use of this lemma.
给出了相应的拟线性方程的定解问题的集中列紧引理 ,利用这一结果得到了方程在无界区域中非平凡解的存在性。
3.
With the mountain pass lemma and the means of straightening the boundary,the existence of nontrivial solutions are obtained by verifing the functional J(u) corresponding to the equations satisfy the local(PS) conditions.
研究了一类含Sobolev-Hardy临界指数与Hardy项的椭圆方程,通过验证方程对应的泛函J(u)满足局部(PS)条件,运用山路引理与拉直边界的方法得到了这类方程非平凡解的存在性。
4) nontrivial solution
非平凡解
1.
Existence of nontrivial solution for an elliptic equation;
一类椭圆型方程的非平凡解的存在性
2.
Existence of nontrivial solutions for the p-Laplacian Problem on unbounded domain;
无界区域上p-Laplace问题的非平凡解的存在性
3.
On the nontrivial solutions and dead core problem for the equation Δu=c︱Du(X)︱~(p-1);
关于方程Δu=c︱Du︱~(p-1)的非平凡解及死核问题
5) non-trivial solution
非平凡解
1.
The relationship between the existence of the non-trivial solutions and the length of normal materials for the one-dimensional Ginzburg-Landau models of superconductivity with S-N-S junctions;
一维含杂质Ginzburg-Landau超导模型非平凡解的存在性与杂质厚度之间的关系
2.
In this paper, we discuss one kind of nonlinear Volterra integral equation with the convolution kernel, and give some results on the uniqueness and approximate method of the non-trivial solutions of this equation.
本文对一类具有卷积核的非线性Ｖｏｌｔｅｒｒａ型积分方程进行了讨论，给出了关于这类方程的非平凡解的存在性和解的逼近方法的一些结果。
3.
The non-trivial solutions of equation λ_1x_1~k+λ_2x_2~k+…+λ_nx_k~n=0 are discussed, and the upper bound of the non-trivial solutions, when k≥6, is given here.
研究了方程λ_1x_1~k+λ_2x_2~k+……+λ_nx_n~k=0的非平凡解,得出了当k≥6时此。
6) trivial solution
平凡解(数)
补充资料：局部平凡纤维丛
局部平凡纤维丛
locally trivial fibre bundle
局部平凡纤维丛【娘.衍州血】翻比elx川山e;，K~0甲H毗田.日.oe PaCc加eH皿e】 纤维为F的纤维丛不X~B(见纤维空间(fibre sPace))，对任意b任B均存在一个邻域U3b和一个同胚甲。:UxF~兀一‘(U)满足兀职。(u，f)=u，其中。‘U，f〔F.映射h。=职石’称为局部平凡丛的一个坐标卡(chart).相应于基空间的覆盖{u}的全体坐标卡{h。}构成局部平凡丛的一个图册(aUas).例如，以局部紧致空间为基空间.Lie群G为群的主纤维丛(pnnc中ai fibre bUndie)即是一个局部平凡纤维丛，其坐标卡h。满足关系 h。(gx)二gh。(x)，戈“二一’(U)，其中G在GxU上的作用由公式g(g‘，。)=(99’，叼给出.给定局部平凡纤维丛兀:X~B和连续映射f:B，~B，相应的诱导纤维丛(让d优ed fibre bull-业)亦局部平凡.
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参考词条