Berestycki-Lions conditions on ground state solutions for a Nonlinear Schrödinger equation with variable potentials [PDF]
Advances in Nonlinear Analysis, 2018 This paper is dedicated to studying the nonlinear Schrödinger equations of the form −△u+V(x)u=f(u),x∈RN;u∈H1(RN), $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(u), & x\in \mathbb{R}^N; \\ u\in H^1(\mathbb{R}^N), \end ...
Sitong Chen, Xianhua Tang
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Advances in Nonlinear Analysis, 2020 This paper deals with the following Choquard equation with a local nonlinear perturbation: −Δu+u=Iα∗|u|α2+1|u|α2−1u+f(u),x∈R2;u∈H1(R2), $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} - {\it\Delta} u+u=\left(I_{\alpha}*|u|^{\frac{\alpha}{2}+1 ...
Sitong Chen, Xianhua Tang, Jiuyang Wei
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Ground state solutions for a quasilinear Kirchhoff type equation
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We study the ground state solutions of the following quasilinear Kirchhoff type equation \[ -\left(1+b\int_{\mathbb{R}^{3}}|\nabla u|^2dx\right)\Delta u + V(x)u-[\Delta(u^2)]u=|u|^{10}u+\mu |u|^{p-1}u,\qquad x\in \mathbb{R}^3, \] where $b\geq 0$ and $\mu$
Hongliang Liu, Haibo Chen, Qizhen Xiao
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Ground State Solutions of Fractional Choquard Problems with Critical Growth
Fractal and Fractional, 2023 In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained.
Jie Yang, Hongxia Shi
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Ground state solutions for quasilinear Schrödinger systems
Journal of Mathematical Analysis and Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Yuxia, Tang, Zhongwei
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Minimal mass blow-up solutions for the $L^2$ critical NLS with inverse-square potential
, 2018 We study minimal mass blow-up solutions of the focusing $L^2$ critical nonlinear Schr\"odinger equation with inverse-square potential, \[ i\partial_t u + \Delta u + \frac{c}{|x|^2}u+|u|^{\frac{4}{N}}u = 0, \] with $N\geqslant 3$ and ...
Csobo, Elek, Genoud, François
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On type I blow up formation for the critical NLW [PDF]
, 2013 We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on $\mathbb{R}^{3+1}$, that is adapted to continuation past type II singularities.
Krieger, Joachim, Wong, Willie
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Ground state solutions for asymptotically periodic fractional Choquard equations
Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is dedicated to studying the following fractional Choquard equation \begin{equation*} (-\triangle)^s u+V(x)u=\left(\int_{\mathbb{R}^N}\frac{Q(y)F(u(y))}{|x-y|^\mu}\mathrm{d}y\right)Q(x)f(u), \qquad u\in H^s(\mathbb{R}^{N}), \end{equation*
Sitong Chen, Xianhua Tang
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Exact ground states of quantum many-body systems under confinement
, 2020 Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential.
del Campo, Adolfo
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Quasilinear Schrödinger equations : ground state and infinitely many normalized solutions
Pacific Journal of Mathematics, 2023 In the present paper, we study the normalized solutions for the following quasilinear Schrödinger equations: $$-Δu-uΔu^2+λu=|u|^{p-2}u \quad \text{in}~\mathbb R^N,$$ with prescribed mass $$\int_{\mathbb R^N} u^2=a^2.$$ We first consider the mass-supercritical case $p>4+\frac{4}{N}$, which has not been studied before.
Li, Houwang, Zou, Wenming
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