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THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN
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作者 陈爽 郭闪闪 许秋菊 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期947-972,共26页
In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p... In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates. 展开更多
关键词 compressible nematic liquid crystals time-periodic solution topological degree theory energy estimates
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Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays 被引量:2
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作者 Jing Liu Pei-Yong Zhu 《Journal of Electronic Science and Technology of China》 2007年第3期238-242,共5页
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generaliz... In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results. 展开更多
关键词 Almost periodic solution cellular neural networks with time-varying delays (CNNVDs) global exponential stability topological degree theory.
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A Note on the Existence of Positive Solutions for a Fourth-Order Semilinear Elliptic System
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作者 Yu Xia GUO Guang Zhong CHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第7期1263-1276,共14页
In this note, we prove the existence of positive solutions to a class of biharmonical systems. Our main ingredients are proving a Liouville type result for biharmonical system in R+^N via the method of moving plane c... In this note, we prove the existence of positive solutions to a class of biharmonical systems. Our main ingredients are proving a Liouville type result for biharmonical system in R+^N via the method of moving plane combined with integral inequality, and establishing a prior estimates for positive solutions of the system via the blowing-up method. 展开更多
关键词 topological degree theory a prior estimate fourth-order system Liouville theorem
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EXISTENCE OF NON-TRIVIAL SOLUTION FOR SUPERLINEAR SYSTEM OF INTEGRAL EQUATIONS AND ITS APPLICATIONS 被引量:10
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作者 张志涛 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1999年第2期153-162,共10页
In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo... In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations. 展开更多
关键词 CONE topological degree theory completely continuous operators superlinear system of equations non-trivial solution.
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Time-Periodic Solution to the Compressible Navier–Stokes/Allen–Cahn System 被引量:1
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作者 Chang Ming SONG Jian Lin ZHANG Yuan Yuan WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2020年第4期419-442,共24页
In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic exter... In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in R^N.The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory,and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force. 展开更多
关键词 Navier–Stokes equation Allen–Cahn equation two-phase flows time-periodic solution topology degree theory
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