Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1048.49004
Anh, L.Q.; Khanh, P.Q.
(Lam Quoc Anh; Phan Quoc Khanh)
Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems. (English)
[J] J. Math. Anal. Appl. 294, No. 2, 699-711 (2004). ISSN 0022-247X

Let $X,M,\Lambda$ be Hausdorff topological spaces, $Y$ be a topological vector space and $C\subseteq Y$ be closed and such that $\text{int}C\neq\emptyset$. Given two multifunctions $K:X\times\Lambda\rightarrow2^{X}$ and $F:X\times X\times M\rightarrow2^{Y}$, the ``parametric vector quasiequilibrium problem'' consists in finding, given $\lambda\in\Lambda$ and $\mu\in M$, some $\bar{x}\in clK(\bar{x},\lambda)$ such that $F(\bar{x} ,y,\mu)\cap(Y\backslash-\text{int}C)\neq\emptyset$ for every $y\in K(\bar{x} ,\lambda)$. \par Assuming that the solution set $S_{1}(\lambda,\mu)$ is nonempty in a neighborhood of $(\lambda_{0},\mu_{0})\in\Lambda\times M$, the present paper gives necessary conditions for the multifunction $S_{1}$ to be lower semicontinuous, or upper semicontinuous. Also, a ``strong'' version of the quasiequilibrium problem is investigated, and sufficient conditions are given for its solution set to be equal to $S_{1}(\lambda,\mu)$. These results generalize and sometimes improve previously known results on quasivariational inequalities.
[Nicolas Hadjisavvas (Hermoupolis)]

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
49J45 Optimal control problems inv. semicontinuity and convergence

Keywords: quasiequilibrium problem; lower semicontinuity; upper semicontinuity; variational inequality; multifunction

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]