Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.     

Some remarks on general commutators theorems

The paper proves some general facts on commutators that refer to Fuglede-Putnam classical theorem in the spectral theory of not necessarily selfadjoint operators.     

Deformations of functionals and bifurcations of extremals

We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established.     

Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

     

Fixed point theorems under the interior condition

We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.

     

The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

几类B值小指标鞅空间的原子分解

本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系.     

极大单调算子的一个邻近点算法

设E是自反的Banach空间,T∶E→2E是极大单调算子.T-10≠.令x0∈E,yn=(J λnT)-1xn en,xn 1=J-1(αnJxn (1-αn)Jyn),n≥0,λn>0,αn∈[0,1],本文研究了{xn}收敛性.     

Banach空间二阶非线性脉冲微分-积分方程的极值解

通过建立一个新的比较定理研究了B anach空间二阶非线性混合型脉冲微分-积分方程初值问题的极值解,所得结果推广和改进了现有文献的主要结果.     

带有弹性碰撞的离散的凝结方程

带有弹性碰撞的离散的凝结方程是反映粒子增长动力学的数学模型，它刻划了这样一种粒子反应系统；系统中任意两个粒子碰撞后一定的概率或者凝结成为更大的粒子，或者发生弹性碰撞．本文研究了这一系统发生冻肢的可能性，并给出了一个充分条件．