The objective of this study was to get some sufficient conditions which guarantee the asymptotic stability and uniform boundedness of the null solution of some differential equations of third order with the variable delay. The most efficient tool for the study of the stability and boundedness of solutions of a given nonlinear differential equation is provided by Lyapunov theory. However the con...

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

We obtain uniform boundedness principles for a new class of families of mappings from topological vector spaces to ordered topological vector spaces. The new class of families of mappings includes the family of linear mappings and many other families which consist of nonlinear mappings. 1 Department of Mathematics, Tianjin University, Tianjin 300072, China. E-mail address: [email protected]...

We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton–Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.