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Continuous dependence for integrodifferential equations with infinite delay
Proceedings of the Indian Academy of Sciences - Section A, 1991The authors show, under certain conditions, that the solution of the integro-differential equation \(x'(t)=h(t,x(t))+\int_{-\infty}^ t q(t,s,x(s))ds+F(t,x(t),Sx(t))\), \(0\leq t\leq T\), \(x(t)=\varphi(t ...
K. Balachandran, Annamalai Anguraj
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Persistence of nonautonomous competitive systems with infinite delay
Acta Mathematicae Applicatae Sinica, 1998The author considers a nonlinear, nonautonomous, nonconvolution-type Volterra system of a particular form. Under suitable assumptions on the kernel and the coefficients it is shown that the system is (1) \(h\)-uniformly bounded (2) uniformly persistent (3) non persistent.
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Existence Theory of NFDE with Infinite Delay
1994The main purpose of this chapter is to present a unified treatment of the local theory of NFDE with infinite delay on a class of comparatively comprehensive phase spaces which contain admissible phase spaces described in the literature and BC-the space of bounded continuous functions which are convenient and useful for the investigation of several ...
Lizhi Wen +2 more
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Delay Equations in Infinite-Dimensional Spaces
2015Our main goal in this chapter is to demonstrate how the method developed in Chapters 2 and 3 can be applied to study qualitative dynamics of abstract evolution equations containing delay terms. These equations naturally arise in various applications, such as viscoelasticity, nuclear reactors, heat flow, neural networks, combustion, interaction of ...
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Semilinear Parabolic Equations with Infinite Delay
1985We shall deal with an abstract semilinear evolution equation $$\dot u\left( t \right) + Au\left( t \right) = F\left( {t,u} \right),{u_0} = \varphi ,$$ (1) with infinite delay, i.e., ut denotes a function ut(s) = u(t+s) on the interval (− ∞, 0]. The motivation for the study of such equations comes partly from theoretical biology.
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Semigroups and differential equations with infinite delay
Nonlinear Analysis: Theory, Methods & Applications, 1981openaire +3 more sources