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Mild Well-posedness of Abstract Differential Equations

In: Functional Analysis and Evolution Equations

Author

Listed:
  • Valentin Keyantuo

    (University of Puerto Rico, Department of Mathematics Faculty of Natural Sciences)

  • Carlos Lizama

    (Universidad de Santiago de Chile, Departamento de Matemática Facultad de Ciencias)

Abstract

We obtain spectral conditions that characterize mild well-posed inhomogeneous differential equations in a general Banach space X. L p periodic solutions of first and second-order equations are considered. The results are expressed in terms of operator-valued Fourier multipliers. Our approach provides a unified framework for various notions of strong and mild solutions. Applications to semilinear equations of second order in Hilbert spaces are given.

Suggested Citation

  • Valentin Keyantuo & Carlos Lizama, 2007. "Mild Well-posedness of Abstract Differential Equations," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 371-387, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_24
    DOI: 10.1007/978-3-7643-7794-6_24
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