Generalization Of An Inequality Of G. Pólya Concerning The Eigenfrequences Of Vibrating Bodies
Generalized Backscattering and the Lax-Phillips Transform
2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the...
Generalized eigenfunctions of relativistic Schrödinger operators in two dimensions.
Generalized Gaudin models and Riccatians
The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is , i=1,..., r, where denote some homogeneous polynomials of degrees constructed from functional variables and their derivatives. It is assumed that . The problem...
Generic simplicity of eigenvalues for a Dirichlet problem of the bilaplacian operator.
Geometry of KDV (1): Addition and the unimodular spectral classes.
This is the first of three papers on the geometry of KDV. It presents what purports to be a foliation of an extensive function space into which all known invariant manifolds of KDV fit naturally as special leaves. The two main themes are addition (each leaf has its private one) and unimodal spectral classes (each leaf has a spectral interpretation).
Global Bifurcation of Waves.
Global bifurcation result for the -biharmonic operator.
Global Instability and Essential Spectrum in Semilinear Evolution Equations.
Global minimizer of the ground state for two phase conductors in low contrast regime
The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap ε between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to ε and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue...
Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.
Global solutions of quasilinear systems of Klein–Gordon equations in 3D
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
Green's function and convergence of Fourier series for elliptic differential operators with potential from Kato space.
Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients
We study the first eigenpair of a Dirichlet spectral problem for singularly perturbed convection-diffusion operators with oscillating locally periodic coefficients. It follows from the results of [A. Piatnitski and V. Rybalko, On the first eigenpair of singularly perturbed operators with oscillating coefficients. Preprint www.arxiv.org, arXiv:1206.3754] that the first eigenvalue remains bounded only if the integral curves of the so-called effective drift have a nonempty ω-limit set. Here we consider...