Premium
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.