Zobrazeno 1 - 10
of 2 042
pro vyhledávání: '"SQUASSINA, A."'
We study concavity properties of positive solutions to the Logarithmic Schr\"odinger equation $-\Delta u=u\, \log u^2$ in a general convex domain with Dirichlet conditions. To this aim, we analyse the auxiliary Lane-Emden problems $-\Delta u = \sigma
Externí odkaz:
http://arxiv.org/abs/2411.01614
Autor:
Gallo, Marco, Squassina, Marco
In this paper we study convexity properties for quasilinear Lane-Emden-Fowler equations of the type $$ \begin{cases} -\Delta_p u = a(x) u^q & \quad \hbox{ in $\Omega$},\\ u >0 & \quad \hbox{ in $\Omega$}, \\ u =0 & \quad \hbox{ on $\partial \Omega$},
Externí odkaz:
http://arxiv.org/abs/2405.05404
In this paper, we are concerned with normalized solutions in $H_{r}^{1}(\mathbb{R}^{3}) \times H_{r}^{1}(\mathbb{R}^{3})$ for Hartree-Fock type systems with the form \be\lab{ Hartree-Fock} \left\{ \begin{array}{ll} -\Delta u +\alpha \phi _{u,v} u=\la
Externí odkaz:
http://arxiv.org/abs/2405.01036
Autor:
Shen, Liejun, Squassina, Marco
We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schr\"{o}dinger systems \[ \left\{ \begin{array}{ll} \displaystyle -\Delta u +A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \newline \displaystyle \part
Externí odkaz:
http://arxiv.org/abs/2403.18014
Autor:
Shen, Liejun, Squassina, Marco
We investigate the existence and concentration of normalized solutions for a $p$-Laplacian problem with logarithmic nonlinearity of type \[ \left\{ \begin{array}{ll} \displaystyle -\varepsilon^p\Delta_p u+V(x)|u|^{p-2}u=\lambda |u|^{p-2}u+|u|^{p-2}u\
Externí odkaz:
http://arxiv.org/abs/2403.09366
We are concerned with solutions of the following quasilinear Schr\"odinger equations \begin{eqnarray*} -{\mathrm{div}}\left(\varphi^{2}(u) \nabla u\right)+\varphi(u) \varphi^{\prime}(u)|\nabla u|^{2}+\lambda u=f(u), \quad x \in \mathbb{R}^{N} \end{eq
Externí odkaz:
http://arxiv.org/abs/2403.01338
We study the fractional Schr\"{o}dinger equations coupled with a neutral scalar field $$ (-\Delta)^s u+V(x)u=K(x)\phi u +g(x)|u|^{q-2}u, \quad x\in \mathbb{R}^3,\qquad (I-\Delta)^t \phi=K(x)u^2, \quad x\in \mathbb{R}^3, $$ where $(-\Delta)^s$ and $(I
Externí odkaz:
http://arxiv.org/abs/2402.12006
In this paper, we study the fractional critical Schr\"{o}dinger-Poisson system \[\begin{cases} (-\Delta)^su +\lambda\phi u= \alpha u+\mu|u|^{q-2}u+|u|^{2^*_s-2}u,&~~ \mbox{in}~{\mathbb R}^3,\\ (-\Delta)^t\phi=u^2,&~~ \mbox{in}~{\mathbb R}^3,\end{case
Externí odkaz:
http://arxiv.org/abs/2402.00464
Autor:
Shen, Liejun, Squassina, Marco
We study a class of planar Schr\"{o}dinger-Poisson systems $$ -\Delta u+\lambda V(x)u+\phi u=f(u) , \quad x\in{\mathbb R}^2,\qquad \Delta \phi=u^2, \quad x\in{\mathbb R}^2, $$ where $\lambda>0$ is a parameter, $V\in C({\mathbb R}^2,{\mathbb R}^+)$ ha
Externí odkaz:
http://arxiv.org/abs/2401.10663
Autor:
Shen, Liejun, Squassina, Marco
We are concerned with the existence of normalized solutions for a class of generalized Chern-Simons-Schr\"{o}dinger type problems with supercritical exponential growth $$ -\Delta u +\lambda u+A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u),\quad \partial_1A_2-
Externí odkaz:
http://arxiv.org/abs/2401.00623