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Functional Differential Equations
1981A distinguishing feature of ordinary differential equations is that the future behavior of solutions depends only upon the present (initial) values of the solution. Numerous physical, economic, biological, and social systems, though, exhibit hereditary dependence. That is, the future state of the system depends not only upon the present state, but also
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Functional Differential Equations
2019Equations determining a functional and involving variational derivatives are called functional differential equations (abbreviated by fde, list in Chap. 1). Definitions and elementary properties of such equations are discussed to prepare the subsequent development on fdes. Two types of such equations are considered: elliptic and parabolic fdes.
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Functional Differential Equations
1968Lyapunov’s second method gives sufficient conditions for stability and asymptotic stability. This method has been extended in several directions.7,8 One of the interesting extension of this method depends basically on the fact that a function satisfying the inequality $$m'(t)\leq w(t,m(t)) \;\;\;\;\;\;\; m(t_{0})=r_{0}$$ is majorized by the ...
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Functional Differential Equations
Functional Differential Equations, 1991T. Yoshizawa, J. Kato
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Neutral Functional Differential Equations
1999The present chapter contains some remarks and ideas concerning application of i—smooth calculus to functional differential equations of neutral type. Taking into account essential features of neutral functional differential equations (NFDE) subsequent elaboration of these aspects requires additional investigating properties of invariant differentiable ...
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DoFun 3.0: Functional equations in mathematica
Computer Physics Communications, 2020Markus Q Huber +2 more
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