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研究定义在向量u=(u~1,…,u~N):Ω■R~n→R~N上的各项异性积分泛函F(u)=∫_Ωf(x,Du(x))dx和非线性椭圆型方程组-Σi=1nDi(aiα(x,Du(x)))=-Σi=1nDiFiα(x),α=1,2,…,N.在密度函数f:Ω×R~(N×n)→R和矩阵a=(a_i~α):Ω×R~(N×n)→R~(N×n)满足某单调不等式条件下,得到u整体有界. 相似文献
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一类二阶迭代泛函微分方程的解析解 总被引:4,自引:0,他引:4
本文研究了一类二阶迭代泛函微分方程x″(z)=mj=0pjxj(z),z∈C.其中m为正整数,xj(z)表示未知函数x(z)的j次迭代,给出了这类方程满足初始条件解析解的几个存在性定理. 相似文献
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针对函数方程f(x)+bf(g(x))=h(x),其中f(x)为待求函数,b为任意实数,h(x)为已知函数,g(x)满足gn(x)=x.经过多次迭代换元,构建由待求函数构成的线性方程组,运用Cramer法则,可得出该函数方程有唯一解的充要条件为bn≠(-1)n,且此时可解出f(x)=1/1-(1-b)nn-1Σi=0(-b)ih(gi(x)). 相似文献
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张萍萍 《数学的实践与认识》2007,37(15):183-188
利用Schrder变换,给出了一类新的时滞变量依赖于状态变量的迭代泛函微分方程的解析解.不但讨论了Schrder变换中常数α在单位圆内和单位根的情况,也给出了α在单位圆上接近于单位根时的结果. 相似文献
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两类线性泛函微分方程解析解的存在性 总被引:1,自引:0,他引:1
解析解的存在性。他将方程解析解的存在性问题转化为寻找一个抽象可分Hilbert空间的非自伴算子的零空间的问题。从而使问题得到顺利的解决。本文利用“优函数”方法给出线性泛函微分方程 相似文献
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一阶迭代泛函微分方程的局部可逆解析解 总被引:1,自引:0,他引:1
本文研究迭代泛函微分方程x′(z)=1/(x(az+b/(x′(z)))),z∈C的解析解,其中a,b均为复常数.首先利用Schr(o|¨)der变换,把迭代泛函微分方程转化为不含迭代的泛函微分方程.针对Schr(o|¨)der变换中的常数α在单位圆上,不是单位根但满足Brjuno条件;α不但在单位圆上,而且是单位根;α在单位圆内三种情况,讨论了辅助方程的解析解.在此基础上,我们证明原方程局部可逆解析解存在,并且计算出解析解表达式.最后举例说明定理的应用. 相似文献
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在共振点附近的一类二阶泛函微分方程的解析解 总被引:3,自引:0,他引:3
在复域C内研究一类包含未知函数迭代的二阶微分方程x″(z)=G(z,x(z),x~2(z),…,x~m(z))解析解的存在性.通过Schr(?)der变换,即x(z)=y(αy~(-1)(z)),把这类方程转化为一种不含未知函数迭代的泛函微分方程α~2y″(αz)y″(z)-αy′(αz)y″(z)= (y′(z))~3G(y(z),y(αz),…,y(α~mz)),并给出它的局部可逆解析解.本文不仅讨论了双曲型情形0<|α|<1和共振的情形(α是一个单位根),而且还在Brjuno条件下讨论了共振点附近的情形(即单位根附近). 相似文献
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§ 1.Introduction Alongwiththedevelopmentofnonlineardynamicalsystems,onehaspaidattentiontonotonlythelong timebehaviourofamovementbutalsoitsprocess,whichtouchesupontheproblemoftheinverseoperationofaniterativeoperation .Byiterativefunctionalequationswemeant… 相似文献
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Existence, uniqueness and stability of Cm solutions of iterative functional equations 总被引:2,自引:0,他引:2
In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x),..., fn(x))=0 (for all x∈J), where J is a connected closed subset of the real number axis R, G∈Cm(Jn+1, R), and n≥2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability of Cm solutions of the above equation for any integer m≥0 under relatively weak conditions, and generalize related results in reference in different aspects. 相似文献
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In this paper a second-order nonautonomous iterative functional differential equation is considered. By reducing the equation with the Schröder transformation to another functional differential equation without iteration of the unknown function, we give existence of its local analytic solutions. We first discuss the case that the constant α given in the Schröder transformation does not lie on the unit circle in C and the case that the constant lies on the circle but fulfills the Diophantine condition. Then we further study the case that the constant is a unit root in C but the Diophantine condition is offended. Finally, we investigate analytic solutions of the form of power functions. 相似文献
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Yu-Qing Chen 《Proceedings of the American Mathematical Society》2001,129(7):2157-2162
We prove the following result. Let be a convex compact subset in a topological vector space, and a convex continuous mapping. (See Definition 1.1.) Then has a fixed point. Moreover, continuous mappings that can be approximated by convex continuous mappings also have the fixed point property.
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By using a well-known fixed point index theorem, we study the existence, multiplicity and nonexistence of positive T-periodic solution(s) to the higher-dimensional nonlinear functional difference equations of the form
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In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability
of the functional equation
6f(x + y) - 6f(x - y) + 4f(3y) = 3f(x + 2y) - 3f(x - 2y) + 9f(2y)6f(x + y) - 6f(x - y) + 4f(3y) = 3f(x + 2y) - 3f(x - 2y) + 9f(2y) 相似文献
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Using the fixed point method, we prove the Hyers Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces. 相似文献
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