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An abstract semilinear first order differential equation in the hyperbolic case

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This paper is devoted to the investigation of the abstract semilinear initial value problem     $du/dt = A(t)u + f(t,u), u(0) = u_0$, in the "hyperbolic" case.
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An abstract nonlinear second order differential equation

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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
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Existence of the fundamental solution of a second order evolution equation

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We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence ${A_n(t)}$ of bounded operators.
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Second order semilinear Volterra integrodifferential equation in Banach space

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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
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Semilinear evolution equations of the parabolic type

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This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
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Second order evolution equations with parameter

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We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter $h ∈ Ω ⊂ ℝ^m$. Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.
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Evolution equations with parameter in the hyperbolic case

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The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter $h ∈ Ω ⊂ ℝ^m$ in the "hyperbolic" case.
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