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- W103693183 abstract "This chapter discusses the existence and stability of solutions on the real line x ( t )+ ƒ t −∞ a( t −τ) g { r , x (τ)) d τ = f ( t ), with general forcing term. It presents an integral and the related integrodifferential equations for real-valued functions on the line. The forcing functions ƒ and Φ are restricted only by the requirement that for each t ∈ R , the function ƒ t ( Φ t ) given on the nonnegative axis R + by s → ƒ t ( s ) = ƒ ( t-s ), s ɛ R + , belongs to a preassigned function space F (or Φ ) on R + . The functions ƒ and x are so related that the present value of the output ƒ depends on the present value of the input x and on all past values of x . The chapter presents a theorem that states that if a : R + → R is nonnegative, nonincreasing, and bounded and g:R × R → R preserves measurability under composition, then whenever the measurable function x: R → R is such that the integral exist for all t ∈ R, Nx is locally absolute continuous." @default.
- W103693183 created "2016-06-24" @default.
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- W103693183 date "1976-01-01" @default.
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- W103693183 title "Existence and Stability of Solutions on the Real Line to x(t) + ∫−∞t a(t−τ)g(τ, x(τ)) dτ=f(t), with General Forcing Term" @default.
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- W103693183 doi "https://doi.org/10.1016/b978-0-12-164902-9.50033-2" @default.
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