We present conditions ensuring the existence of possibly nonsmooth upper and lower functions for the periodic boundary value problem ″ = () = (0), (2), ′(0) = ′(2). This enables us to obtain new existence and multiplicity results for regular and singular periodic boundary value problems

We define a modulo one rational number invariant of order up to 2 as the Arf invariant of the -hyperbolic quadratic function of every infinite cyclic covering of every (possibly non-orientable) compact 3-manifold, and analogously a modulo one rational number invariant of order up to 4 as an...

In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic in an appropriate, digital, computational language. In...

We derive scalar boundary integral equation formulas for both interior and exterior biharmonic equations with the Dirichlet boundary data. They are based on indirect boundary integral equation formulas, so called the and formulas. The scalar formulas are derived through an unconventional...

We consider the planar three-body problem and prove that, besides some exceptional cases, in a neighborhood of the Lagrangian particular solution for this problem, there is no an additional meromorphic first integral

The following problem of rectilinear routing is studied: given pairs of points on a surface and a set of permissible orthogonal paths joining them, whether is it possible to choose a path for each pair avoiding all intersections. We prove that if each pair has one or two possible paths to join...

We consider the dynamic process of an elastic body submitted to unilateral contact and friction with a rigid foundation. Friction is modelized with a Coulomb law with a coefficient possibly depending on the slip velocity. To keep a possibility of velocity discontinuities we use the elastodynamic...

Several singular limits are investigated in the context of a 2 × 2 system arising . in the modeling of chromatographic processes. In particular, we focus on the case where the relaxation term and a projection operator are concentrated on a discrete lattice by means of a Dirac comb. This...

In our previous workfll], a relation between Tsukiyama problem about self homotopy equivalence was found by using a generalization of phantom map. In this note , fundamental result is established for such a generalization. This is the first time one can deal with phantom maps to space not...