相关论文: Three solutions to discrete anisotropic problems w…

The multiple-solution problem in determining the three-interfering-resonances' parameters from a fit to an experimentally measured distribution is considered in a mathematical viewpoint. In this paper it is shown that there are four…

We obtain a pair of nontrivial solutions for a class of concave-linear-convex type elliptic problems that are either critical or subcritical. The solutions we find are neither local minimizers nor of mountain pass type in general. They are…

We are concerned with the existence of infinitely many radial symmetric solutions for a nonlinear stationary problem driven by a new class of nonhomogeneous differential operators. Our proof relies on the symmetric version of the mountain…

The Cauchy problem for a quasi-linear parabolic equation with a small parameter at a higher derivative is considered. The initial step-like function contains another small parameter. Formal asymptotic solutions of the problem in small…

Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…

We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…

We construct a two-parameter family of explicit solutions to the cubic wave equation on $\mathbb{R}^{1+3}$. Depending on the value of the parameters, these solutions either scatter to linear, blow-up in finite time, or exhibit a new type of…

In this paper, we study the existence and multiplicity of positive solutions for a nonlinear fourth-order with multi-point boundary conditions involving an integral boundary condition. The main tool is Krasnosel'skii fixed point theorem on…

We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…

We show that scale invariant scattering theory allows to exactly determine the critical points of two-dimensional systems with coupled $O(N)$ and Ising order pameters. The results are obtained for $N$ continuous and include criticality of…

We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations…

Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite…

We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions,…

We establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and…

We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of…

The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…

This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…

The dynamical instability of relativistic polytropic spheres, embedded in a spacetime with a repulsive cosmological constant, is studied in the framework of general relativity. We apply the methods used in our preceding paper to study the…