Extension of Beckert's Continuation Method to Variational Inequalities

Erich Miersemann, Hans Mittelmann

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A theoretical foundation is given for a recently proposed continuation method for parameter‐dependent nonlinear variational inequalities in Hilbert space. The second derivative of one of the functional in the inequality is assumed to generate a quadratic form that is equivalent to the norm of the Hilbert space. The value of this functional is used as continuation parameter. Existence of local continuations is shown using a generalization of Beckert's continuation method for eigenvalue equations and extending continuation results obtained recently by the nuthors. In addition, uniqueness and monotonicity results are proven for these continuations.

Original languageEnglish (US)
Pages (from-to)183-195
Number of pages13
JournalMathematische Nachrichten
Volume148
Issue number1
DOIs
StatePublished - 1990

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Continuation Method
Variational Inequalities
Continuation
Hilbert space
Second derivative
Quadratic form
Monotonicity
Uniqueness
Eigenvalue
Norm

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Extension of Beckert's Continuation Method to Variational Inequalities. / Miersemann, Erich; Mittelmann, Hans.

In: Mathematische Nachrichten, Vol. 148, No. 1, 1990, p. 183-195.

Research output: Contribution to journalArticle

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