Related papers: Existence results for the conformal Dirac-Einstein…
The dynamic response of a parametric system constituted by a spin precessing in a time dependent magnetic field is studied by means of a perturbative approach that unveils unexpected features, and is then experimentally validated. The…
We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…
The Breit interaction is implemented in the no-pair variational Dirac-Coulomb (DC) framework using an explicitly correlated Gaussian basis reported in the previous paper [Paper I: P. Jeszenszki, D. Ferenc, and E. M\'atyus (2022)]. Both a…
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson…
We prove the existence of one or more solutions to a singularly perturbed elliptic problema with two potential functions.
This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
Complete constraint analysis and choice of gauge conditions consistent with equations of motion is done for Abelian Chern Simons field interacting minimally with a complex scalar field. The Dirac-Schwinger consistency condition is satisfied…
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.
New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…
This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…
We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance…
An analytical solution of the Dirac equation with a Cornell potential, with identical scalar and vectorial parts, is presented. The solution is obtained by using the linear potential solution, related to Airy functions, multiplied by…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
We define a new class of partial differential equations of first order (complex covariantly equipped systems of equations), which are invariant with respect to (pseudo)orthogonal changes of cartesian coordinates of (pseudo)euclidian space.…
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…
In this paper we consider the first order discrete Hamiltonian system $$\begin{cases} x_1(n+1)-x_1(n)& =- H_{x_2}(n,x(n)), x_2(n)-x_2(n-1)& =\ \ H_{x_1}(n,x(n)). \end{cases} $$ Where $n\in \mathbb{Z}$, $x(n)=$ $x_1 (n) \choose x_2 (n)$$ \in…
Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property but their energy functional is unbounded both lower and…