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Zbl 0808.35039
Bosák, Miroslav
Bifurcation of stationary solutions to quasivariational inequalities. (English)
[J] Math. Bohem. 119, No.1, 21-42 (1994). ISSN 0862-7959

A bifurcation problem for quasivariational inequalities of the type $$u\in K(u),\qquad (\lambda u-Au -G(\lambda, u),v- u)\geq 0 \quad \forall v\in K(u) \tag $*$ $$ is considered. Here $\{K(u)$; $u\in H\}$ is a system of closed convex sets in the real Hilbert space $H$ satisfying certain assumptions, $A: H\to H$ is a linear completely continuous operator, $G: \bbfR\times H\to H$ a small compact perturbation, $\lambda$ a real bifurcation parameter. The existence of bifurcation points of $(*)$ lying in intervals $(\lambda\sb 1, \lambda\sb 2)$ is proved where $\lambda\sb 1$, $\lambda\sb 2$ are eigenvalues of a certain type of the operator $A$. Moreover, it is shown that under certain assumptions there exists a bifurcation point of $(*)$ greater than the greatest real eigenvalue of the operator $A$. This can occur even in case of a symmetric operator $A$. Notice that this is excluded if $A$ is symmetric and $K(u) =K$ is a fixed closed convex cone with the vertex at the origin, i.e. if $(*)$ is a standard variational inequality.
[M.Kučera (Praha)]

MSC 2000:: *35J85 Unilateral problems; variational inequalities (elliptic type)
35B32 Bifurcation (PDE)

Keywords: unilateral problems; quasivariational inequalities

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