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51.
Boris S. Mordukhovich Bingwu Wang 《Journal of Mathematical Analysis and Applications》2003,282(1):63-84
In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions. 相似文献
52.
徐明跃 《数学的实践与认识》2004,34(6):172-176
首先给出 Banach空间为逼近紧的几何特征 .然后用随机变量组成的 Banach空间及空间中预报集的几何性质给出预报算子连续的条件 . 相似文献
53.
J. P. Raymond 《Journal of Optimization Theory and Applications》1990,67(1):109-132
We give existence theorems of solutions for Lagrange and Bolza problems of optimal control. These results are obtained without convexity assumptions on the cost function with respect to the control variable. We extend a Cesari's theorem to cost functions which are nonlinear with respect to the space variable and to problems which are governed by a differential inclusion. Moreover, we consider the case where the control variable belongs to a space of measurable functions and the case where this variable belongs to a Lebesgue space. 相似文献
54.
Arthur W. Apter 《Mathematical Logic Quarterly》2007,53(1):78-85
If κ < λ are such that κ is indestructibly supercompact and λ is 2λ supercompact, it is known from [4] that
- {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness}
- {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ satisfies level by level equivalence between strong compactness and supercompactness}
55.
许兴业 《高校应用数学学报(A辑)》2017,32(4)
研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质. 相似文献
56.
57.
nAbstract Let p 0 and μ be a normal function on [0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ [0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1. 相似文献
58.
Positive ground state of coupled systems of Schrödinger equations in
involving critical exponential growth
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João Marcos do Ó José Carlos de Albuquerque 《Mathematical Methods in the Applied Sciences》2017,40(18):6864-6879
In this paper, we study the existence of a positive ground state solution to the following coupled system of nonlinear Schrödinger equations: where the nonlinearities f1(x,s) and f2(x,s) are superlinear at infinity and have exponential critical growth of the Trudinger‐Moser type. The potentials V1(x) and V2(x) are nonnegative and satisfy a condition involving the coupling term λ(x), namely, λ(x)2<δ2V1(x)V2(x) for some 0<δ<1. For this purpose, we use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap argument and Lq‐estimates, we get regularity and asymptotic behavior. 相似文献
59.
60.
杜刚 《数学的实践与认识》2017,(8):235-241
讨论了全空间上一类带Hardy-Sobolev项的拟线性椭圆问题,利用集中紧原理和适当的实验函数,得到并验证了(PS)_c条件,从而证明了该问题非平凡解的存在性. 相似文献