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A Generalized existence theorem of Backward Doubly Stochastic Differential Equations

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1525-1534页

作者： Qian LIN School of Mathematics Shandong University Ji'nan 250100 P. R. China and Laboratoire de Mathematiques CNRS UMR 6205 Universite de Bretagne Occidentale6avenue Victor Le Gorgeu CS 93837 29238 Brest cedex 3 France

In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.

关键词： Backward doubly stochastic differential equations comparison theorem existence theorem backward stochastic integral

ON THE existence theorem OF NON-TRIVIAL PERIODIC SOLUTION OF PERIODIC SYSTEMS OF HIGH ORDER

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Acta Mathematicae Applicatae Sinica 1990年第1期6卷 40-43页

作者：赵晓强 Institute of Applied Mathematics Academia Sinica China

In this paper, we consider nonlinear and nonautonomous systems with the trivial solution:dx/dt=f(t, x), x∈R~nwhere f(t+ω,x)+f(t, x), f(t, 0)=0. By using the theory of Brouwer topological degree, we obtainthe existen... 详细信息

关键词： Periodic Solution existence theorem Trivial Solution Periodic System Math Application

A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

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Science China Mathematics 2024年第2期67卷 315-338页

作者： Shengda Zeng Akhtar A.Khan Stanislaw Migórski Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Faculty of Mathematics and Computer Science Jagiellonian University in Krak´owKrak´ow 30348Poland Center for Applied and Computational Mathematics School of Mathematical SciencesRochester Institute of TechnologyRochesterNY 14623USA College of Sciences Beibu Gulf UniversityQinzhou 535000China

In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.

关键词： generalized quasi-variational inequality existence theorem optimal control Kakutani-Ky Fan theorem Oseen problem non-Newtonian fluid nonmonotone slip boundary condition

Several existence theorems for Positive Radial Solutions to a Semilinear Elliptic BVP

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Northeastern Mathematical Journal 2001年第2期17卷 169-174页

作者：姚庆六 Department of Mathematics Northwest Normal University Lanzhou 730070

The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|existence criterion and ... 详细信息

The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.

关键词： second order elliptic equation Dirichlet BVP in annulus positive radial solution existence theorem

Brill-Noether Theory for Rank Two Vector Bundles Generated by Their Sections

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Acta Mathematica Sinica,English Series 2008年第12期24卷 1995-2010页

作者： Jian Do XIAO Xiao Jiang TAN School of Mathematical Sciences Peking University Beijing 100871 P. R. China School of Mathematics Southwest Jiaotong University Chengdu 611756 P. R. China LMAM and School of Mathematical Sciences Peking University Beijing 100871 P. R. China

We here study the Brill-Noether theory for rank two vector bundles generated by their sections. We generalize the vanishing theorem, the Clifford theorem and the existence theorem to such bundles.

关键词： rank two vector bundle vanishing theorem Clifford theorem existence theorem

Reflected Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients

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Acta Mathematica Sinica,English Series 2013年第4期29卷 639-650页

作者： Zhi LI Jiao Wan LUO School of Information and Mathematics Yangtze University School of Mathematics and Information Sciences Guangzhou University

In this paper, we study one-dimensional reflected backward doubly stochastic differential equations （RBDSDEs） with one continuous barrier and discontinuous （left or right continuous） genera- tor. We obtain an exis... 详细信息

关键词： Reflected backward doubly stochastic differential equations existence theorem comparison theorem

A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS

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Acta Mathematica Scientia 2015年第6期35卷 1386-1400页

作者： H.M.SRIVASTAVA 罗旻杰 R.K.RAINA Department of Mathematics and Statistics University of Victoria Department of Mathematics East China Normal University Department of Mathematics M.P.University of Agriculture and Technology

In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.

关键词： Laplace transform Sumudu transform natural transform H-function H- transform inversion formula Parseval-type relationship existence theorem Borel-Dzrbashjan transform Fubini's theorem Weierstrass's test Heaviside generalized function

FIfth-ORDER ISOTROPIC DESCARTES TENSOR

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Applied Mathematics and Mechanics(English Edition) 2000年第4期21卷 395-398页

作者：阎大桂徐军严尚安付诗禄 Department of Mathematics Logistical Engineering University Chongqing P R China

Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.

关键词： descartes tensor isotropic tensor existence theorem representation theorem structure theorem

existence of Multiple Positive Solutions for Fourth Order Two-point Boundary Value Problems

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Northeastern Mathematical Journal 2002年第1期18卷 63-72页

作者：戚仕硕 Department of Mathematics Zhengzhou University Zhengzhou 450052

The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples ... 详细信息

关键词： existence theorem multiple positive solution fourth-order boundary value problem