The nonlinear differential equation x" = f(t, x(t)), f being 22T-periodic in t, is considered for the existence of 27T-periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.

Let Wn be a random walk on the locally free group with m generators subject to periodic boundary conditions, and let T (Wn) be the set of removable elements. We prove that limn→∞ E(#T (Wn)) m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik et. al. [3]) that the limit tends to 1 3 as m → ∞.

In this paper, we consider one-dimensional attractor of a non-autonomous second order strongly damped lattice system with periodic driving force under Neumann boundary condition or periodic boundary condition. We obtain the existence of a global attractor and prove this attractor is homeomorphic to the circle.

In this paper we prove a Hölder and Lipschitz stability estimates of determining the residual stress by a single pair of observations from a part of the lateral boundary or from the whole boundary. These estimates imply first uniqueness results for determination of residual stress from few boundary measurements.

In this paper we prove existence results for extremal solutions of the first order discontinuous impulsive differential inclusions with periodic boundary conditions and impulses at the fixed times under certain monotonicity conditions of the multi-valued functions.

We construct examples, that log Hölder continuity of the integrated density of states cannot be improved. Our examples are limit-periodic.

In two-dimensional lattice fermion model a determinant representation for the twopoint correlation function of the twist field in the disorder phase is obtained. This field is defined by twisted boundary conditions for lattice fermion field. The large distance asymptotics of the correlation function is calculated at the critical point and in the scaling region. The result is compared with the v...

We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an infinite dimensional dynamical system and establish the existence of a compact attractor and a finite dimensional inertial manifold that contains it. Moreover, Gevrey regularity of solutions on the attractor is established and used to prove that four nodes are determining for each solution on the attractor...

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(−1) space can fail to be either injective or surjective.

— We prove that the subquartic wave equation on the three dimensional ball Θ, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in ∩s<1/2H (Θ). We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed in our previous work [6] and invariant measure considerations w...