Results 41 to 50 of about 1,711 (146)
Abstract and Applied Analysis, 2013 We study the quasilinear Schrödinger equation of the form , . Under appropriate assumptions on and , existence results of nontrivial solutions and high energy solutions are obtained by the dual-perturbation method.
Yu Chen, Xian Wu
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Boundary Value Problems, 2019 The application of the new criteria for minimally thin sets with respect to the Schrödinger operator to an approximate solution of singular Schrödinger-type boundary value problems are discussed in this study.
Bo Meng
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Finite time blow-up for a one-dimensional quasilinear parabolic–parabolic chemotaxis system [PDF]
, 2010 International ...
Cieślak, Tomasz, Laurençot, Philippe
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper, we study the following quasilinear Schrödinger equation \begin{equation*} \begin{split} -\Delta u&+V(x)u-\kappa u\Delta(u^2)+\mu\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\\ &+\mu\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s ...
Yingying Xiao, Chuanxi Zhu
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The mirror mode: A "superconducting'' space plasma analogue
, 2018 We examine the physics of the magnetic mirror mode in its final state of saturation, the thermodynamic equilibrium, to demonstrate that the mirror mode is the analogue of a superconducting effect in a classical anisotropic-pressure space plasma.
Baumjohann, W., Treumann, R. A.
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Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling [PDF]
, 2016 We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons.
Carbone, Francesco +2 more
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Ground states of Nehari-Pohožaev type for a quasilinear Schrödinger system with superlinear reaction
Electronic Research Archive, 2023 This article is devoted to study the following quasilinear Schrödinger system with super-quadratic condition: $ \begin{equation*} \left\{\begin{matrix} -\Delta u+V_{1}(x)u-\Delta (u^{2})u = h(u,v),\ x\in \mathbb{R}^{N},\\ -\Delta v+V_{2}(x)v-\Delta (v^
Yixuan Wang, Xianjiu Huang
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Standing waves with a critical frequency for nonlinear Choquard equations
, 2016 In this paper, we study the nonlocal Choquard equation $$ -\varepsilon^2 \Delta u_\varepsilon + V u_\varepsilon= (I_\alpha * |u_\varepsilon|^p)|u_\varepsilon|^{p-2}u_\varepsilon $$ where $N\geq 1$, $I_\alpha$ is the Riesz potential of order $\alpha \in ...
Van Schaftingen, Jean, Xia, Jiankang
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Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we consider the quasilinear Schrödinger system in $\mathbb R^{N}$ ($N\geq3$): \begin{equation*} \begin{cases} -\Delta u+ A(x)u-\frac{1}{2}\Delta(u^{2})u=\frac{2\alpha }{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+ Bv-\frac{1}{2}\
Jianqing Chen, Qian Zhang
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Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities
, 2014 We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We
Ambrosetti +31 more
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