Abstract We consider what we term existence-constrained semi-infinite programs. They contain a finite number of (upper-level) variables, regular objective, and existence constraints. These constraints assert that for all (medial-level) variable values from set infinite cardinality, there must exist (lower-level) second satisfy an inequality. Existence-constrained programs are generalization pro...

We consider amathematical model in the form of a system of ordinary differential equations (ODE) foroptimally administrating cancer treatments. The ODE systemdynamics characterized by locating equilibrium points and stability propertiesare determined by linearization and usingappropriate Lyapunovfunctions. By applying optimal control theory, we seek to minimize the cost function associated with...

We show that a model describing the interaction between normal and infectious prion proteins admits global solutions. More precisely, supposing the involved degradation rates to be bounded, we prove global existence and uniqueness of classical solutions. Based on this existence theory, we provide sufficient conditions for the existence of global weak solutions in the case of unbounded splitting...

We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence, and asymptotic behavior of non-oscillatory solutions of the equation. Our results extend and generalize the known ...

If (M, g) is a Lorentz manifold and S a spacelike hypersurface, let h and k denote the induced metric and second fundamental form of S respectively. The mean curvature of S is the trace trhk. An interesting class of spacelike hypersurfaces are those whose mean curvature is constant (CMC hypersurfaces). The Lorentz manifolds of primary interest in the following are those which possess a compact ...