Extension of Beckert's Continuation Method to Variational Inequalities | Zendy

Miersemann Erich | Zendy; Mittelmann Hans D. | Zendy

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Extension of Beckert's Continuation Method to Variational Inequalities

Author(s) -

Miersemann Erich,

Mittelmann Hans D.

Publication year - 1990

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.3211480111

Subject(s) - mathematics , continuation , hilbert space , uniqueness , monotonic function , norm (philosophy) , variational inequality , generalization , nonlinear system , eigenvalues and eigenvectors , mathematical analysis , extension (predicate logic) , quadratic equation , pure mathematics , physics , geometry , quantum mechanics , computer science , political science , law , programming language

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.

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