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WAVEFRONT SOLUTIONS IN THE DIFFUSIVE NICHOLSON'S BLOWFLIES EQUATION WITH NONLOCAL DELAY
Zhang, Cun-Hua The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.1
In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).
WAVEFRONT SOLUTIONS IN THE DIFFUSIVE NICHOLSON’S BLOWFLIES EQUATION WITH NONLOCAL DELAY
Cun-Hua Zhang 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1
In the present article we consider the diffusive Nicholson’s blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain R. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed byWang, Li and Ruan (J. Differential Equations,222(2006), 185-232).
NONLOCAL FRACTIONAL DIFFERENTIAL INCLUSIONS WITH IMPULSE EFFECTS AND DELAY
NAWAL A. ALSARORI,KIRTIWANT P. GHADLE 한국산업응용수학회 2020 Journal of the Korean Society for Industrial and A Vol.24 No.2
Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.
SEMILINEAR NONLOCAL DIFFERENTIAL EQUATIONS WITH DELAY TERMS
Jeong, Jin-Mun,Cheon, Su Jin Korean Mathematical Society 2013 대한수학회지 Vol.50 No.3
The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.
Semilinear nonlocal differential equations with delay terms
정진문,천수진 대한수학회 2013 대한수학회지 Vol.50 No.3
The goal of this paper is to obtain the regularity and theexistence of solutions of a retarded semilinear differential equation withnonlocal condition by applying Schauder’s fixed point theorem. We constructthe fundamental solution, establish the H¨older continuity resultsconcerning the fundamental solution of its corresponding retarded linearequation, and prove the uniqueness of solutions of the given equation.
Existence of Solutions of Fuzzy Delay Differential Equations with Nonlocal Condition
BALACHANDRAN, K.,PRAKASH, P. 한국산업정보응용수학회 2002 한국산업정보응용수학회 Vol.6 No.1
In this paper we prove the existence of solutions of fuzzy delay differential equations with nonlocal condition. The results are obtained by using the fixed point principles.
PARK, Dong-Gun,SON, K.D.,KWUN, Young-Chel The Honam Mathematical Society 2004 호남수학학술지 Vol.26 No.4
In this paper, sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed point theorem and the resolvent operator. Example is provided to illustrate the theory.
Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay
Jun Zhou 대한수학회 2020 대한수학회지 Vol.57 No.1
A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.
BIFURCATION ANALYSIS OF A SINGLE SPECIES REACTION-DIFFUSION MODEL WITH NONLOCAL DELAY
Zhou, Jun Korean Mathematical Society 2020 대한수학회지 Vol.57 No.1
A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.