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 lipschitz连续
 lipschitz continuous
 Kirchhoff Equation with Lipschitz Continuous Coefficient 具有Lipschitz连续系数的Kirchhoff方程 短句来源 The existence of positive solutions has been discussed for the nonlinear boundary value problem y″+f(y)=0,y(0)=0 , and y(1)=b>0, where f is a locally Lipschitz continuous, f(0)≥0 and may change signs. 基于Leray Schauder度理论和上下解方法讨论非线性边值问题 y″ +f( y) =0 ,y( 0 )=0 ,y( 1) =b>0的正解存在性 ,其中 f是局部Lipschitz连续函数 f( 0 )≥ 0 ,并且可以是变号函数 . 短句来源 Let X be an arbitrary real Banach space and T : X →X be a Lipschitz continuous accretive operator. 设X是任意实Banach空间,T:X→X是Lipschitz连续的增生算子. 短句来源 Let X be an arbitrary real Banach space and T∶X→X be a Lipschitz continuous accretive operator. 设X是一实Banach空间,且T:X→X是Lipschitz连续的增生算子。 短句来源 Let X be an arbitrary real Banach space and T: XX be a Lipschitz continuous accretive operator. 设X是任意实Banach空间,T:XX是Lipschitz连续的增生算子. 短句来源 更多
 lipschitz continuity
 In the forth part, we mainly discuss the properties of cosine operators, such as the normcontinuity, locally Lipschitz continuity, which are preserved under the multiplicative perturbation with the (Z)-condition. 第四部分讨论了余弦算子在(Z)条件下的乘积扰动和扰动下的不变性。 如(Z)条件下的乘积扰动仍保持范数连续、局部Lipschitz连续不变。 短句来源 About the nonlinear differential operator which preserves strongly monotone and Lipschitz continuity , the result is similar. Under some conditions , the error estimate of RKPM is presented for some nonlinear elliptic boundary problem. 如果一阶非线性微分算子是强单调，Lipschitz连续的，也得到了最小二乘无网格方法的误差估计，对于非线性椭圆方程边值问题，在满足一定的条件下，得到了RKPM方法的误差估计。 短句来源 Under the Lipschitz continuity and g- strong monotonicity of the underlying mapping,we give the global error bound of the general variational inequalities,and prove that the predictor stepsizes have a uniformly positive bound from below. 在所含函数L ipsch itz连续和g-强单调的条件下讨论了广义变分不等式的全局误差界,并证明了预估步长的一致有正下界性。 短句来源 The concept of η-partially relaxed Lipschitz continuity for mappings is introduced. By applying the concept and the auxiliary variational inequality technique, we study a new class of generalized set-valued nonlinear mixed variational-like inequalities in reflexive Banach spaces. We also prove an existence theorem of solutions for the class of generalized set-valued nonlinear mixed variational-like inequalities and suggest an innovative iterative algorithm to compute the approximate solutions of the class of variational inequalities. 对映射引入了η-部分松弛Lipschitz连续的概念,应用这个概念和辅助变分不等式的技巧,在自反Banach空间中研究了一类广义集值非线性混合似变分不等式,给出了这类变分不等式解的存在性证明及算法,并讨论了算法的收敛性. 短句来源
 “lipschitz连续”译为未确定词的双语例句
 The main results are as follows:Theorem 2.1 For each 0 ≤ t < T, φ(t, ·) is locally Lipschitz . 定理2.1 对于每个0≤tLipschitz连续的。 短句来源 THE QUANTITATIVE PROPERTIES OF NONLINEAR LIPSCHITZIAN OPERATORS(Ⅱ) THE GLB DAHLQUIST CONSTANT 非线性Lipschitz连续算子的定量性质（Ⅱ）——glb┐Dahlquist数 短句来源 Qualitative Studies on Nonlinear Lipschitz Operators(Ⅳ)-Spectral Theory 非线性Lipschitz连续算子的定量性质（Ⅳ）──谱理论 短句来源 Ω. p (x)is Lip-schitz continuous onΩand satisfies 2 < p ~-≤p( x)≤p~+ Ω的有界区域, p (x)在Ω上Lipschitz连续并满足2 < p~-≤p( x)≤p~+ 短句来源 Quantitative Study of Nonlinear Lipschitz Operators in C~m Space C~m空间中非线性Lipschitz连续算子的定量性质 短句来源 更多

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 lipschitz continuous
 It is proved that the constituted algorithm with either Wolfe-type or Armijo-type line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter μ and continuously differentiable on J × J for any μ >amp;gt; 0. The existence of an exponential attractor is proved under the abstract assumption that the right-hand side is Lipschitz continuous. It has also been proved that the space of fractional integration, the space of Lipschitz continuous functions and the Sobolev space are identical in L2-norm. It is proved that the efficient portfolio's composition is a Lipschitz continuous, differentiable mapping of these parameters under suitable conditions. 更多
 lipschitz continuity
 In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented. Subdifferentiability and lipschitz continuity in experimental design problems Lipschitz continuity of the global design function is proved and conditions for strict differentiability are given. Finally, we use these results in the analysis of Lipschitz continuity for solutions of parametric quadratic programs. 更多
 The Newton method x_(n+1) = u(x_n), ?n ∈ N_0, where u(x) = x -- p'(x)~(-1) p(x), is wide-ly used in solving nonlinear equations P(x) = 0 and its every kind of improvement dependson the generalizing iteration function u(x) to w(x, z) = x -- P'(z)~(-1) P(x). The methodx_(n+1) = w (x_n, (1/2)(x_n + y_n)), y_(n+1) = w (x_(n+1), (1/2)(x_n + y_n) ), which is proposed by Kingand Werner is convergent with order 1 + 2~(1/2) and keeps the function evaluations the sameas those of Newton's. In this paper we prove the following.... The Newton method x_(n+1) = u(x_n), ?n ∈ N_0, where u(x) = x -- p'(x)~(-1) p(x), is wide-ly used in solving nonlinear equations P(x) = 0 and its every kind of improvement dependson the generalizing iteration function u(x) to w(x, z) = x -- P'(z)~(-1) P(x). The methodx_(n+1) = w (x_n, (1/2)(x_n + y_n)), y_(n+1) = w (x_(n+1), (1/2)(x_n + y_n) ), which is proposed by Kingand Werner is convergent with order 1 + 2~(1/2) and keeps the function evaluations the sameas those of Newton's. In this paper we prove the following. Let P: D ? C~N → C~N be twice Frechet differentiable on a convex subset D with ||P"(x) ||≤M and ||P"(x) -- P"(x')||≤L||x -- x'|| ?x, x'∈ D. Assume that x_0 ∈ D, x_1 = u(x_0),M + (7/12)L_η ≤K, h = Kβ_η ≤(1/2), S≡ {x| ||x -- x_1||≤η(1--(1--2h)~(1/2))/(1 + (1--2h)~(1/2))}?D. Then x_n and y_n generated by King--Werner's procedure belong to S and are convergentto the solution of equations with N variables P(x) = 0. The corresponding conclusion holdsalso for King--Werner's procedure with y_0 ≠ x_0. 解非线性方程组P(x)=0的Newton叠代法S_(n+1)=u(x_n)的种种改进与其叠代函数u(x)=x-P’(x)~(-1) P(x)由一目拓广到两目ω(x,z)=x-P’(z)~(-1)P(x)有关,King-Werner的改进方案x_(n+1)=w(x_n, 1/2(x_n+y_n)),y_(n+1)=w(x_(n+1),1/2(x_n+y_n))保持计值量不变而使收敛阶达到1+2~(1/2),我们证明了,设P:D? C~N→C~N在凸区域D上具有以L为常数的Lipschitz连续的二阶Frechet导数P″(x),||P″x||≤M x∈D,?x_0∈D,x_1=u(x_0),||x_1-x_0||≤η, ||P’(x_0)~(-1)||≤β,M+1/12Lη≤K,h=Kβη≤1/2,S≡{x|||x-x_1||≤η(1-(1-2h)~(1/2)/(1+(1-2h)~(1/2))}?D,则King-Werner叠代过程产生的x_n和y_n都属于S并且收敛于N元方程组P(x)=0的解,这个结论,与关于Newton叠代过程收敛性的Ostrowski-定理十分相似。 In this paper, we consider the stochastic integral equations with respect to semi-mastingales X = Φ(X) + F (X) M Under the continuous condition of local lipschitz and with the growth con- dition added, the existence of a unique solution is proved. 本文在严加安［１］的基础上，讨论半鞅积分方程 Ｘ＝Φ（Ｘ）＋Ｆ（Ｘ）．Ｍ解的存在唯一性．我们所获得的存在唯一性定理，与［１］中定理１３．１３相比较，不要求Ｆ、Φ满足Ｌｉｐｓｃｈｉｔｚ连续条件，而仅要求它们满足局部Ｌｉｐｓｃｈｉｔｚ连续条件，但我们附加了所谓的增长条件．我们还给出解过程估计式．此外，还给出Ｄｏｌｅａｎｓ－Ｄａｄｅ方程解的另一存在唯一性定理。 In this paper,we shall investigate the existences of periodic solutionsfor nonlinear wave equations with a dissipative term in form(?) where ω is a positive constant,f and g have periodic ω in t.The main result of this paper is that if f is Lipschitz continuous in(u,u_i,u_x)with a Lipschitz constantl(t),herel(t)is a continuous func-tion with periodic ω,and the continuous function g with periodic ω int satisfies the condition:(?)→0,uniformly about(t,x)and ifM(β)exp{M(β)∫_0~ω(?)(t)dt-β/2ω}0<|β|<2,then the question(*)has... In this paper,we shall investigate the existences of periodic solutionsfor nonlinear wave equations with a dissipative term in form(?) where ω is a positive constant,f and g have periodic ω in t.The main result of this paper is that if f is Lipschitz continuous in(u,u_i,u_x)with a Lipschitz constantl(t),herel(t)is a continuous func-tion with periodic ω,and the continuous function g with periodic ω int satisfies the condition:(?)→0,uniformly about(t,x)and ifM(β)exp{M(β)∫_0~ω(?)(t)dt-β/2ω}0<|β|<2,then the question(*)has ω—periodic solutions,where M(β)is α positive constant only depending on β, 本文讨论了带耗散项的非线性波动方程的周期解的存在问题,方程的形式为(?)其中ω是正常数,f 和 g 关于 fω—周期主要结论为:若 f 关于(u,u_t u_x)Lipschitz 连续,其 Lipschitz 常数是—ω周期函数(?)(t).满足M(β)exp(?)θ<|β|<2,M(β)是仅依赖于β的正常数;g 满足(?)则问题(*)有解。 << 更多相关文摘
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