Differential Equations and Mathematical Physics

Analytical solutions for ordinary and partial differential equations.- On the ratio of the first two eigenvalues of Schrödinger operators with positive potentials.- Inverse scattering for self-adjoint nth order differential operators on the line.- On the dirichlet index conjecture.- Three-dimensional inverse scattering.- Spectral properties of Schrodinger operators with trapping potentials in the semi-classical limit.- Discrete sets of coherent states and their use in signal analysis.- Information, uncertainty and the singular value decomposition of the filtered fourier transformation.- On Schrödinger operators with von Neumann-Wigner type potentials.- Nonlinear conservative systems.- The initial value problem for the nonlinear equations for zero Mach number combustion.- Longtime solutions for a class of convection diffusion systems.- A closed form for the symbol of the resolvent parametrix of an elliptic operator.- Existence and finite-dimensionality of attractors for the Landau-Lifschitz equations.- The coulomb potential in higher dimensions.- A regularity theorem for differential equations of constant strength.- Intermittent bifurcation of vortex flows.- Remarks on the Scattering problem for nonlinear Schrödinger equations.- Asymptotics of solutions and spectra of perturbed periodic Hamiltonian systems.- Behavior of eigenfunctions and the spectrum of Schrödinger operators.- Shape resonances in quantum mechanics.- Random perturbation theory and quantum chaos.- Path integral for a Weyl quantized relativistic Hamiltonian and the nonrelativistic limit problem.- Scattering with penetrable wall potentials.- Commutator methods and asymptotic completeness for a new class of stark effect Hamiltonians.- Asymptotics of the Titchmarsh-Weyl m-coefficient for integrablepotentials, II.- On the difference between eigenvalues of Sturm-Liouville operators and the semi-classical limit.- Finite element approximation to singular minimizers, and applications to cavitation in non-linear elasticity.- On relating generalized expansions to fourier integrals.- Link between periodic pctentials and random potentials in one-dimensional Schrödinger operators.- Undressing of odd pseudodifferential operators.- Some mathematical aspects of the wavemaker theory.- Integro-differential equations associated with piecewise deterministic processes.- Ambrosetti-Prodi type results in nonlinear boundary value problems.- Transmutation of analytic and harmonic functions.- Some solved and unsolved canonical problems of diffraction theory.- Runge-Kutta schemes and numerical instabilities: The logistic equation.- Structure of positive solutions to (??+V) u=0 in Rn.- An extension of Lavine's formula for time-delay.- Some open questions in multi-dimensional inverse problems.- Radially symmetric solutions of a Monge-Ampère equation arising in a reflector mapping problem.- Scattering theory for the wave equation on a hyperbolic manifold.- On unsteady flow in a two-dimensional cascade with in-passage shocks.- On the absorption of singularities in dissipative nonlinear equations.- Feedback control for an abstract parabolic equation.- Approximate solution of random differential equation.- Geometric properties and bounds for positive solutions of semilinear elliptic equations.- Asymptotic completeness of multiparticle scattering.- On a multi-dimensional inverse problem related to the Gel'fand-Levitan theory.- Fundamental solution of the Poisson-Boltzmann equation.- Examples of exponential decay of eigenfunctions of mangetic Schrödinger operators.- Spatially localizedfree vibrations of certain semilinear wave equations on ?2: Recent results and open problems.