Related papers: Notes on Multiple Periodic Solutions for Second-or…
We discuss two different methods of obtaining ``effective $2 \times 2$ Hamiltonians'' of the electromagnetic interaction which include relativistic corrections. One is the standard Foldy--Wouthuysen transformation which we compare with the…
We investigate the existence of collision-free nonconstant periodic solutions of the $N$-vortex problem in domains $\Omega\subset\mathbb{C}$. These are solutions $z(t)=(z_1(t),\dots,z_N(t))$ of the first order Hamiltonian system \[…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
We prove the existence of globally H\"{o}lder continuous solutions to certain elliptic partial differential equations with lower-order terms. Our result is applicable to coefficients controlled by a negative power of the distance from the…
We study the existence of families of periodic solutions in a neighbourhood of a symmetric equilibrium point in two classes of Hamiltonian systems with involutory symmetries. In both classes, involutions reverse the sign of the Hamiltonian…
We study the {\it Hamiltonian elliptic system} \begin{eqnarray}\label{HS1-abstract} \left\{ \begin{aligned} -\Delta u & = \lambda |v|^{r-1}v +|v|^{p-1}v \qquad &\hbox{in} \ \ \Omega ,\\ -\Delta v & = \mu |u|^{s-1}u +|u|^{q-1}u \qquad…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…
Firstly,we generalize the classical Palais-Smale-Cerami condition for $C^1$ functional to the local Lipschitz case,then generalize the famous Benci-Rabinowitz's and Rabinowitz's Saddle Point Theorems with classical Cerami-Palais-Smale…
An improved finite difference method with compact correction term is proposed to solve the Poisson equations. The compact correction term is developed by a coupled high-order compact and low-order classical finite difference formulations.…
We define the non-commutative multiple bi-orthogonal polynomial systems, which simultaneously generalize the concepts of multiple orthogonality, matrix orthogonal polynomials and of the bi-orthogonality. We present quasideterminantal…
In this paper we study the problem of almost periodicity of solutions for dissipative differential equations (Bronshtein's conjecture). We give a positive answer to this conjecture for monotone almost periodic systems of…
The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
The existence and spatio-temporal patterns of $2\pi$-periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2) \times \Gamma \times \mathbb Z_2$-equivariant…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the…