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The semilinear Cauchy problem (1) u’(t) = Au(t) + G(u(t)), $u (0) = x \in \bar{D (A)}$ , with a Hille-Yosida operator A and a nonlinear operator G: D(A) → X is considered under the assumption that ||G(x) - G(y)|| ≤ ||B(x -y )|| ∀x,y ∈ D(A) with some linear B: D(A) → X, $B {(λ - A)}^{- 1} x = λ \int_{0}^{\infty} e^{- λ t} V (s) x d s$ , where V is of suitable small strong variation on some interval [0,ε). We will prove the existence of a semiflow on $[0, \infty) \times \bar{D (A)}$ that provides Friedrichs solutions in L₁ for (1). If X is a Banach lattice, we replace the condition above by |G(x) - G(y)| ≤ Bv whenever...

On the complex formation approach in modeling predator prey relations, mating, and sexual disease transmission.

Thieme, Horst R.; Yang, Jinling — 2000

Electronic Journal of Differential Equations (EJDE) [electronic only]

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The Asymptotic Behaviour of Solutions of Nonlinear Integral Equations.

Renewal theorems for linear discrete Volterra equations.

On a Class of Hammerstein Integral Equations.

On the Boundedness and the Asymptotic Behaviour of the Non-Negative Solutions of Volterra-Hammerstein Integral Equations.

Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations.

Semilinear perturbations of Hille-Yosida operators

On the complex formation approach in modeling predator prey relations, mating, and sexual disease transmission.