Time decay of scaling invariant Schroedinger equations on the plane [PDF]
, 2014 We prove the sharp L^1-L^{\infty} time-decay estimate for the 2D-Schroedinger equation with a general family of scaling critical electromagnetic potentials.
arxiv +1 more source
On Kirchhoff-Schrödinger-Poisson-type systems with singular and critical nonlinearity
Advances in Nonlinear AnalysisThis work focuses on the Kirchhoff-Schrödinger-Poisson-type system with singular term and critical Sobolev nonlinearity as follows: −a+b∫Ω∣∇u∣pdxΔpu+ϕ∣u∣q−2u=λu−γ+∣u∣p∗−2uinΩ,−Δϕ=∣u∣qinΩ,u=ϕ=0on∂Ω,\left\{\begin{array}{ll}-\left(a+b\mathop{\displaystyle ...
Yang Baoling, Zhang Deli, Liang Sihua
doaj +1 more source
Semiclassical limit for nonlinear Schroedinger equations with electromagnetic fields [PDF]
arXiv, 2001 We prove some multiplicity results by means of a perturbation technique in critical point theory.
arxiv
Single--peaks for a magnetic Schrödinger equation with critic al growth [PDF]
arXiv, 2006 We prove existence results of complex-valued solutions for a semilinear Schr\"odinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory.
arxiv
Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations
Alexandria Engineering Journal, 2021 In this paper, we consider two kinds of nonlinear Schrödinger equations with the fractional Laplacian and Hardy potential (λ|x|s ...
Guotao Wang +3 more
doaj
On Local Perturbations of SCHRÖdinger Operator on Plane [PDF]
arXiv, 2002 We obtain necessary and sufficient conditions for emerging of small eigenvalue for Schr\"odinger operator on plane under local operator perturbations. In the case the eigenvalue emerges we construct its asymptotics. The examples are given.
arxiv
Extremal first Dirichlet eigenvalue of doubly connected plane domains and dihedral symmetry [PDF]
, 2007 We deal with the following eigenvalue optimization problem: Given a bounded domain $D\subset \R^2$, how to place an obstacle $B$ of fixed shape within $D$ so as to maximize or minimize the fundamental eigenvalue $\lambda_1$ of the Dirichlet Laplacian on $
Kiwan, Rola, Soufi, Ahmad El
core +2 more sources
Distribution of particles which produces a desired radiation pattern [PDF]
arXiv, 2005 A method is given for calculation of a distribution of small particles, embedded in a medium, so that the resulting medium would have a desired radiation pattern for the plane wave scattering by this medium.
arxiv
Eigenvalue estimates for the one-particle density matrix [PDF]
arXiv, 2020 It is shown that the eigenvalues $\lambda_k, k=1, 2, \dots,$ of the one-particle density matrix satisfy the bound $\lambda_k\le C k^{-8/3}$ with a positive constant $C$.
arxiv
Quasilinear elliptic equations with critical potentials
Advances in Nonlinear Analysis, 2017 We study Liouville theorems for problems of the ...
D’Ambrosio Lorenzo, Mitidieri Enzo
doaj +1 more source