Results 21 to 30 of about 15,857,552 (384)
Energy-critical NLS with potentials of quadratic growth [PDF]
, 2017 Consider the global wellposedness problem for nonlinear Schr\"odinger equation \[ i\partial_t u = [-\tfrac{1}{2} \Delta + V(x)] u \pm |u|^{4/(d-2)} u, \ u(0) \in \Sigma(\mathbf{R}^d), \] where $\Sigma$ is the weighted Sobolev space $\dot{H}^1 \cap |x|^{
Jao, Casey
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Asymptotic analysis for fourth order Paneitz equations with critical growth [PDF]
, 2011 We investigate fourth order Paneitz equations of critical growth in the case of $n$-dimensional closed conformally flat manifolds, $n \ge 5$. Such equations arise from conformal geometry and are modelized on the Einstein case of the geometric equation ...
Hebey, Emmanuel, Robert, Frédéric
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Concentrating solutions for a fractional Kirchhoff equation with critical growth [PDF]
Nonlinear Fractional Schrödinger Equations in R^N, 2018 In this paper we consider the following class of fractional Kirchhoff equations with critical growth: ( ε 2 s a + ε 4 s − 3 b ∫ R 3 | ( − Δ ) s 2 u | 2 d x ) ( − Δ ) s u + V ( x ) u = f ( u ) + | u | 2 s ∗ − 2 u in R 3 , u ∈ H s ( R 3 ) , u > 0 in R 3 ...
V. Ambrosio
semanticscholar +1 more source
Electronic Journal of Differential Equations, 2021 In this article, we study a class of critical fractional Schrodinger-Poisson system with two perturbation terms. By using variational methods and Lusternik-Schnirelman category theory, the existence of ground state and two nontrivial solutions are ...
Lintao Liu, Kaimin Teng
doaj
Semiclassical states for Choquard type equations with critical growth: critical frequency case [PDF]
Nonlinearity, 2017 In this paper we are interested in the existence of semiclassical states for the Choquard type equation −ε2Δu+V(x)u=∫RNG(u(y))|x−y|μdyg(u)inRN, where 0 < μ < N, N ⩾ 3, ɛ is a positive parameter and G is the primitive of g which is of critical growth due ...
Yanheng Ding, Fashun Gao, Minbo Yang
semanticscholar +1 more source
Multi-bump solutions for the magnetic Schrödinger–Poisson system with critical growth
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we are concerned with the following magnetic Schrödinger–Poisson system \begin{align*} \begin{cases} -(\nabla+i A(x))^{2}u+(\lambda V(x)+1)u+\phi u=\alpha f(\left | u\right |^{2})u+\vert u\vert^{4}u,& \text{ in }\mathbb{R}^{3}, \\ -\Delta \
Chao Ji +2 more
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Understanding Homogeneous Nucleation in Solidification of Aluminum by Molecular Dynamics Simulations [PDF]
, 2017 Homogeneous nucleation from aluminum (Al) melt was investigated by million-atom molecular dynamics (MD) simulations utilizing the second nearest neighbor modified embedded atom method (MEAM) potentials.
Baskes, Michael I. +2 more
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Advanced Nonlinear Studies, 2021 We study the asymptotic profile, as ℏ→0{\hbar\rightarrow 0}, of positive solutions ...
Cassani Daniele, Wang Youjun
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Positive solutions of a Kirchhoff–Schrödinger--Newton system with critical nonlocal term
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper deals with the following Kirchhoff–Schrödinger–Newton system with critical growth \begin{equation*} \begin{cases} \displaystyle-M\left(\int_{\Omega}|\nabla u|^2dx\right)\Delta u=\phi |u|^{2^*-3}u+\lambda|u|^{p-2}u, &\rm \mathrm{in ...
Ying Zhou +3 more
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Concentration results for a magnetic Schrödinger-Poisson system with critical growth
Advances in Nonlinear Analysis, 2020 This paper is concerned with the following nonlinear magnetic Schrödinger-Poisson type ...
Liu Jingjing, Ji Chao
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