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The existence and stability of solutions of nonlinear operator differential equations

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Abbreviations

A :

nonlinear operator

D(A) :

Domain of A

\(\overline {D(A)}\) :

closure of D(A)

H :

Hilbert space with inner product (·,·)

H 1 :

Hilbert space with inner product (·,·)1

I :

identity operator

M :

positive number

R(A) :

range of A

S :

bounded linear operator

{T t};t≧0:

family of nonlinear semi-group

V(x, y) :

defining sesquilinear functional

υ(x(t)) :

derivative of v(x(t)) at point t≧0

x, y, z :

elements of H

x e :

equilibrium solution

α,β, γ,δ,λ :

real numbers

→ :

strong convergence

\(\xrightarrow{w}\) :

weak convergence

(·,·) 1 :

equivalent inner product to (·,·)

References

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Author information

Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh

    C. V. Pao

Authors
  1. C. V. Pao
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Additional information

Communicated by C.-C. Wang

This paper is a part of the author's doctoral dissertation at the University of Pittsburgh, Pittsburgh, Pennsylvania, 1968, supported by NASA under Grant Number NGR 39-011-039. The author acknowledges his gratitude towards his advisers Professor G. Laush and Professor W. G. Vogt for their many valuable suggestions.

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Pao, C.V. The existence and stability of solutions of nonlinear operator differential equations. Arch. Rational Mech. Anal. 35, 16–29 (1969). https://doi.org/10.1007/BF00248492

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  • DOI: https://doi.org/10.1007/BF00248492

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