相关论文: Stable solutions of symmetric systems involving hy…

This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to…

We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013,…

We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential…

In this paper we extend the interior regularity results for stable solutions in [Cabr\'{e}, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)] to operators with variable coefficients. We show that stable solutions to the semilinear…

We prove the existence of axially symmetric solutions to the Vlasov--Poisson system in a rotating setting for sufficiently small angular velocity. The constructed steady states depend on Jacobi's integral and the proof relies on an implicit…

This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through…

We present solutions for the (constant and spectral-parameter) Yang-Baxter equations and Yang-Baxter systems arising from algebra structures and discuss about their symmetries. In the last section, we present some applications.

We find a new method for looking for the static and spherically symmetric solutions in $F(R)$ theory of gravity. With this method, a number of new solutions in terms of the analytic functions are obtained. We hope this investigation may be…

We study the symmetry properties for solutions of elliptic systems of the type {ll}-\dive(a_1(x,|\nabla u^1|(X))\nabla u^1(X))=F_{1}(x, u^1(X),..., u^n(X)), ... -\dive(a_n(x,|\nabla u^n|(X))\nabla u^n(X))=F_{n}(x, u^1(X),..., u^n(X)), where…

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

A static axisymmetric solution with an additional cylindrical symmetry is considered and that the matter consists in a cosmological and a dust term.

The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…

We examine the stability of the elliptic solutions of the focusing nonlinear Schr\"odinger equation (NLS) with respect to subharmonic perturbations. Using the integrability of NLS, we discuss the spectral stability of the elliptic…

We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…

In this paper some existence results for the minimal P-symmetric periodic solutions are proved for first order autonomous Hamiltonian systems when the Hamiltonian function is superquadratic, asymptotically linear and subquadratic. These are…

We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…

In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator…

In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…

In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schr\"odinger equation near anti-continuous limit. Our novel insight is that the analysis of linearized operator, usually…

We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher…