Related papers: Revisiting second-order linear differential equati…
In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.
A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…
It is shown that solutions of the Cauchy for the fourth-order thin film equation becomes non-oscillatory and non-sign-changing precisely at and above the heteroclinic bifurcation point n=1.75987..., so that, possibly, these solutions begin…
It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is…
The periodic homogenization problem of integro-differential equations of the alpha stable L{\'e}vy operators is studied in this paper. Thanking to the symmetry of the L{\'e}vy density, we can use the method of the formal asymptotic…
The first result of our article is another proof of Mertens' third theorem in the number field setting, which generalises a method of Hardy. The second result concerns the sign of the error term in Mertens' third theorem. Diamond and Pintz…
We establish and prove a fixed point theorem from which some sufficient conditions on the existence of positive almost periodic solutions for a model of hematopoiesis with oscillatory circulation loss rate are deduced. Some particular…
Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for…
In this article we have studied complex linear homogeneous difference equations where the coefficients are meromorphic functions, having finite iterated p-phi order. We have made some estimations on the growth of its nontrivial solutions.…
Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in [15] even for symmetric convex…
A model of memristor-based Chuas oscillator is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria. Bifurcational mechanisms of oscillation excitation are explored for different forms of…
We establish the Hyers-Ulam stability of a second-order linear Hill-type $h$-difference equation with a periodic coefficient. Using results from first-order $h$-difference equations with periodic coefficient of arbitrary order, both…
An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, and derived from a much later form of the solution. A linear ansatz…
We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…