Minimax Results with Respect to Different Altitudes in the Situation of Linking

Consider a continuous function on a metric space. In the presence of linking between a compact pair and a closed set, depending on the different behaviors of the function on the linking sets, we establish minimax results guaranteeing existence of Palais-Smale sequences or providing gradient estimates. Our approach relies on deformation techniques

Uniqueness results for a Dirichlet problem with variable exponent

We study the uniqueness of weak solutions for Dirichlet problems with variable exponent and non-standard growth conditions. First, we provide two uniqueness results under ellipticity type hypotheses. Next, we provide a uniqueness result when the operator driving the problem is in the form of the divergence of a monotone map. Finally, we derive a fourth uniqueness result under homogeneity type hypotheses, by means of a comparison result and approximation

Dynamics of Controlled Hybrid Systems of Aerial Cable-Ways

Dynamics of the hybrid systems of aerial cable-ways is investigated. The eigenvalue problems are considered for such hybrid systems with different assumptions. An overview of different methods for eigenvalue problems is given. In the research, the method of the normal fundamental systems is applied, which turns out to be very effective for the considered problems. Changes of dynamical characteristics of the systems depending on the controlled parameter are studied.Comment: Accepted (15-May-2006) to the Proceedings of the "International Conference of Hybrid Systems and Applications", The University of Louisiana, Lafayette, LA, USA, May 22-26 2006, to be published in the journal "Nonlinear Analysis: Hybrid Systems and Applications

A version of Zhong's coercivity result for a general class of nonsmooth functionals

A version of Zhong's coercivity result (1997) is established for nonsmooth functionals expressed as a sum Φ+Ψ, where Φ is locally Lipschitz and Ψ is convex, lower semicontinuous, and proper. This is obtained as a consequence of a general result describing the asymptotic behavior of the functions verifying the above structure hypothesis. Our approach relies on a version of Ekeland's variational principle. In proving our coercivity result we make use of a new general Palais-Smale condition. The relationship with other results is discussed

Existence Results for Constrained Quasivariational Inequalities

We deal with a constrained quasivariational inequality under a general form. We study existence of solutions in two situations depending on whether the set of constraints is bounded or possibly unbounded