Nonlinear perturbation of linear evolution equations in a banach space

  • W. E. Fitzgibbon


Let X be a Banach space and {A(t)|t ε [0, T]} a family of closed linear, densely defined m-accretive operators in X. This paper is concerned with the additive perturbation of {A(t)|t ε [0, T]} by a continuous family of nonlinear accretive operators {B(t)|t ε [0, T]}. Namely solutions are provided for the integral equation u(t, τ, x) = W(t, τ)x −\(\mathop \smallint \limits_\tau ^t \)W(t, s)B(s) · · u(s, τ, x)ds, u(τ, τ, x) = x where W(t, s) is the linear evolution operator associated with the linear differential equation v'(t, s, x) + A(t)v(t, s, x) = 0, v(s, s, x) = x.


Differential Equation Banach Space Integral Equation Evolution Equation Evolution Operator 
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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • W. E. Fitzgibbon
    • 1
  1. 1.Houston

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