Zobrazeno 1 - 10
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pro vyhledávání: '"Cardoso, Mykael"'
Autor:
Gomes"", "Andressa, Cardoso", "Mykael
We consider the initial value problem for the inhomogeneous nonlinear Schr\"odinger equation with double nonlinearities (DINLS) \begin{equation*} i \partial_t u + \Delta u = \lambda_1 |x|^{-b_1}|u|^{p_1}u + \lambda_2|x|^{-b_2}|u|^{\frac{4-2b_2}{N-2}}
Externí odkaz:
http://arxiv.org/abs/2408.10866
Autor:
Cardoso, Mykael, Farah, Luiz Gustavo
We consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^N$ \begin{align}\label{inls} i \partial_t u +\Delta u +V(x)|u|^{\frac{4-2b}{N}}u = 0, \end{align} where $V(x) = k(x)|x|^{-b}$, with $b>0$. Under suitable assumptions
Externí odkaz:
http://arxiv.org/abs/2408.08825
We are interested in finding prescribed $L^2$-norm solutions to inhomogeneous nonlinear Schr\"{o}dinger (INLS) equations. For $N\ge 3$ we treat the equation with combined Hardy-Sobolev power-type nonlinearities $$ -\Delta u+\lambda u=\mu|x|^{-b}|u|^{
Externí odkaz:
http://arxiv.org/abs/2407.09737
In this work, we consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^n$ \begin{align} i\partial_t u + \Delta u + \gamma |x|^{-b}|u|^{\alpha} u = 0, \end{align} where $\gamma=\pm 1$, and $\alpha$ and $b$ are positive numb
Externí odkaz:
http://arxiv.org/abs/2309.04029
In this paper we study the focusing inhomogeneous 3D nonlinear Schr\"odinger equation with inverse-square potential in the mass-supercritical and energy-subcritical regime. We first establish local well-posedness in $\dot{H}_a^{s_c}\cap \dot{H}_a^1$,
Externí odkaz:
http://arxiv.org/abs/2305.06971
In this paper, we propose a gradient type term for the $k$-Hessian equation that extends for $k>1$ the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan-Kramer chang
Externí odkaz:
http://arxiv.org/abs/2301.07201
Autor:
Cardoso, Mykael, Farah, Luiz Gustavo
We consider the $L^2$ critical inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^N$ $$ i \partial_t u +\Delta u +|x|^{-b} |u|^{\frac{4-2b}{N}}u = 0, $$ where $N\geq 1$ and $0
Externí odkaz:
http://arxiv.org/abs/2108.11434
Autor:
Cardoso, Mykael, Farah, Luiz Gustavo
In this paper we consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation \begin{align}\label{inls} i \partial_t u +\Delta u +|x|^{-b} |u|^{2\sigma}u = 0, \,\,\, x \in \mathbb{R}^N \end{align} with $N\geq 3$. We focus on the intercritical c
Externí odkaz:
http://arxiv.org/abs/2105.10748
Autor:
Campos, Luccas, Cardoso, Mykael
Consider the focusing inhomogeneous nonlinear Schr\"odinger equation in $H^1(\mathbb{R}^N)$, $$iu_t + \Delta u + |x|^{-b}|u|^{p-1}u=0,$$ when $b > 0$ and $N \geq 3$ in the intercritical case $0 < s_c <1$. In previous works, the second author, as well
Externí odkaz:
http://arxiv.org/abs/2104.11266
We consider the inhomogeneous biharmonic nonlinear Schr\"odinger (IBNLS) equation in $\mathbb{R}^N$, $$i \partial_t u +\Delta^2 u -|x|^{-b} |u|^{2\sigma}u = 0,$$ where $\sigma>0$ and $b>0$. We first study the local well-posedness in $\dot H^{s_c}\cap
Externí odkaz:
http://arxiv.org/abs/2011.04715