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The Global Existence of Nonlinear Evolutionary Equation with Small Delay

Xunwu Yin
2012 Journal of Applied Mathematics  
We investigate the global existence of the delayed nonlinear evolutionary equation∂tu+Au=f(u(t),u(t−τ)). Our work space is the fractional powers spaceXα.  ...  Under the fundamental theorem on sectorial operators, we make use of the fixed-point principle to prove the local existence and uniqueness theorem.  ...  Acknowledgments This work is supported by NNSF of China 11071185 and NSF of Tianjin 09JCYBJC01800 .  ... 
doi:10.1155/2012/257140 fatcat:jo73yloakndmlm5tds5lceeckq

Qualitative Analysis on Differential, Fractional Differential, and Dynamic Equations and Related Topics

Said R. Grace, Taher S. Hassan, Shurong Sun, Elvan Akin
2016 Discrete Dynamics in Nature and Society  
Yuan et al. introduced and analyzed split-step theta (SST) method for nonlinear neutral stochastic differential delay equations (NSDDEs).  ...  Akin investigate the asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations.  ...  Yuan et al. introduced and analyzed split-step theta (SST) method for nonlinear neutral stochastic differential delay equations (NSDDEs).  ... 
doi:10.1155/2016/3590319 fatcat:7s6zim5v7bdgpoiomgn6sje2gq

Page 6299 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
of solutions of some differential equations with an unbounded delay.  ...  P.| (RS-PERM; Perm’) On the asymptotic behavior of solutions of a system of linear functional-differential equations with delay and periodic parameters. (Russian) Izv. Vyssh. Uchebn. Zaved.  ... 

Page 5618 of Mathematical Reviews Vol. , Issue 87j [page]

1987 Mathematical Reviews  
The main results are: (i) a uniform ultimate L®-bound for solutions of (1), if 2 C R, for any delay; (ii) a uniform ultimate bound in L?  ...  The author considers the question of ultimate uniform bounded- ness for nonnegative solutions of the logistic equation with dif- fusion and delay: (1) u,(z,t) — Au(z,t) < f(u(z,t),u(z,t —7)), u > 0, in  ... 

Page 3051 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
Joachim Escher, Smooth solutions of nonlinear elliptic systems with dynamic boundary conditions (173-183); H. O.  ...  Priiss, Linear evolutionary integral equations on the line (485-513); I. A. Shishmarév and P. I.  ... 

Page 5743 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Solutions of the approximate free boundary problem are compared with nu- merical solutions of the full system of diffusion-reaction equations and shown to be in good agreement.” 94j:35177 35Q72 35B35 73B30  ...  The authors are concerned with a system of nonlinear partial dif- ferential equations, in short, the coupled Cahn-Hilliard equations, describing the nonisothermal phase separation of a two-component system  ... 

Mathematical Theories and Applications for Nonlinear Control Systems

Xue-Jun Xie, Ju H. Park, Hiroaki Mukaidani, Weihai Zhang
2019 Mathematical Problems in Engineering  
Meng entitled "Stability Analysis of Solutions for a Kind of Integro-Differential Equations with a Delay" analyzes the stability of the zero solution for second-order integrodifferential equations with  ...  By adopting the exp(−Φ( )) method, five different solutions of the STFmKdV equation are obtained. S.  ...  The editors also wish to thank the anonymous reviewers for their careful reading of the manuscripts submitted to this special issue collection and their many insightful comments and suggestions.  ... 
doi:10.1155/2019/2065786 fatcat:qx66v5pu3fgo7ee4rt7rn6rcj4

Page 1712 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Existence and uniqueness of the solutions of nonautonomous delay equations. (English summary) Far East J. Math. Sci. 5 (1997), no. 4, 579-600.  ...  The main results are as follows: (i) Equation (1) has a positive bounded solution if and only if ri tp(t)dt < oo.  ... 

Page 1363 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
= A(0). i=0 Some sufficient conditions for the nonoscillatory solutions and bounded oscillatory solutions of equation (*) to tend to zero as t — +00 are obtained.  ...  (BG-PLOV) Numeric-analytic method for finding the periodic solutions of nonlinear differential-difference equations with impulses. Mathematica (Cluj) 32(55) (1990), no. 1, 19-25.  ... 

Page 1770 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Well-posedness and approximation results for a special class of semilinear evolution equations, which also incorporates delay equations with state and time-dependent delays, are discussed in Chapter 11  ...  equations with nonlinear perturbations.  ... 

Page 5134 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
of the Riccati equation A'P + PA — PBB'P+C'C+G'G=0.  ...  In this note, the uniform stabilization of the linear evolutionary system x’ = Ax + Bu, x(0) = x9, is considered.  ... 

Advances in Nonlinear Analysis and Optimization

Jein-Shan Chen, Gue Myung Lee, Mohamed A. Tawhid
2013 Abstract and Applied Analysis  
Solution set is analyzed, and properties of merit function for such complementarity problems including level bounded set property and error bounds are investigated. The article by H. Qinghai and Z.  ...  They also point out that their method can be considered for functional equations and system of nonlinear equations. The article by L.  ... 
doi:10.1155/2013/439012 fatcat:kgk55f2g7bc3fe7bwgueny6uga

Page 3397 of Mathematical Reviews Vol. 58, Issue 5 [page]

1979 Mathematical Reviews  
Evolutionary equations: Pierre Charrier, “Pointwise degeneracy” for delay evolutionary equations (pp. 81-86); J. A.  ...  McCalla, Exact solutions of some functional differential equations (pp. 163-168). Chapter 5.  ... 

Page 3134 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
Edelson and Ramin Vakil- ian, Bounded entire solutions of higher-order semilinear equations (pp. 207-214); Uri Elias, Minors of the Wronskian of the differen- tial equation L,, y + p(x)y = 0 and their  ...  Grammatikopoulos, Behavior of the nonoscillatory solutions of first order neutral delay differential equations (pp. 265-272); John R. Graef, Paul W. Spikes, L. Hat- vani and J.  ... 

Page 3141 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
Differential Equations 12 (1972), 63-80; MR 48 #6574], the author establishes the existence of a homeomorphism between bounded solutions of the two systems. J. S. W. Wong (Hong Kong) Mickens, R.  ...  A survey of known results with applications to various types of evolution equations including delay and Volterra types. {For the entire collection see MR 83h:34002.}  ... 
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