A resolvent for an iteration method for nonlinear partial differential equations

Author:
J. W. Neuberger

Journal:
Trans. Amer. Math. Soc. **226** (1977), 321-343

MSC:
Primary 47H99; Secondary 35A35, 35R20

DOI:
https://doi.org/10.1090/S0002-9947-1977-0425705-X

MathSciNet review:
0425705

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Abstract: For each of *m* and *n* a positive integer denote by the space of all real-valued symmetric *i*-linear functions on . Denote by *L* a nonzero linear functional on , denote by *f* a real-valued analytic function on and denote by a member of . Denote by *H* the space of all real-valued functions *U*, analytic at the origin of , so that . For for all *x* for which this is defined. A one-parameter semigroup (nonlinear if ) *K* on *H* is constructed so that if , then converges, as , to a solution *Y* to the partial differential equation . A resolvent *j* for this semigroup is determined so that also converges to *y* as and so that converges to as . The solutions of are precisely the fixed points of the semigroup *K*.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1977-0425705-X

Keywords:
Semigroup of nonlinear transformations,
resolvent,
nonlinear partial differential equations

Article copyright:
© Copyright 1977
American Mathematical Society