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Behaviour of solutions of nonlinear alternative problems under perturbations of the linear part with rank change

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1107)

Abstract

This paper is concerned with the behaviour of solutions of nonlinear operator equations with non-invertible linear part under perturbations of the operators involved. Even in the linear case, the solutions need not change continously if the linear part is perturbed in such a way that its rank changes. We prove a continuous-dependence result for the nonlinear problem and illustrate it with an example involving the behaviour of periodic solutions of nonlinear differential equations at resonance under perturbations of the differential operator.

Keywords

  • Banach Space
  • Linear Operator
  • Periodic Solution
  • Nonlinear Problem
  • Bounded Linear Operator

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References

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© 1984 Springer-Verlag

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Engl, H.W. (1984). Behaviour of solutions of nonlinear alternative problems under perturbations of the linear part with rank change. In: Vinti, C. (eds) Nonlinear Analysis and Optimization. Lecture Notes in Mathematics, vol 1107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101494

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  • DOI: https://doi.org/10.1007/BFb0101494

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13903-4

  • Online ISBN: 978-3-540-39123-4

  • eBook Packages: Springer Book Archive