In this paper we are concerned with the existence of invariant curves planar twist mappings which almost periodic in a spatial variable. As an application result to differential equations will prove solutions and boundedness all for superlinear Duffing’s equation external force.

Existence and boundedness is proved for the solutions of a boundary value problem two-dimensional Broadwell model in rectangle. The influence orientation relation to sides rectangle on form analysed. Exact are found use determine accommodation coefficients at boundaries fluid flow rectangular box.

We extend previous results on boundedness of sets coherent sheaves a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us prove properness properties Douady space as well related semistability such existence Harder-Narasimhan filtrations.

Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and technology. Recently a well developed stability theory of functional differential systems has come into existence [15-21]. Qualitative properties of impulsive differential equations have been intensively researched for years. In [3-11], by using lyapunov...

A study of the boundedness in probability of the set of possible wealth outcomes of an economic agent facing constraints, and with limited access to information, is undertaken. The wealth-process set is abstractly structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integrator. We obtain the equiva...

Abstract We study a nonlocal Robin–Venttsel’-type problem for the regional fractional p -Laplacian in an extension domain $$\Omega $$ Ω with boundary d -set. prove existence and uniqueness of strong solution via semigroup approach. Markovianity ultracontractivity properties are proved. then consider elliptic pr...

Gronwall-Bellman inequalities and their various linear and nonlinear generalizations play very important roles in the discussion of existence, uniqueness, continuation, boundedness, and stability properties of solutions of differential equations and difference equations. The literature on such inequalities and their applications is vast. For example, see 1–12 for continuous cases, and 13–20 for...

We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As corollaries, we provide approaches towards birational boundedness and boundedness of anti-canonical volumes of varieties of -Fano type. Furthermore, we show b...

We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class...

We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence and uniqueness of a global-in-time smoot...