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pro vyhledávání: '"Cassani, Daniele"'
\noindent We are concerned with positive normalized solutions $(u,\lambda)\in H^1(\mathbb{R}^2)\times\mathbb{R}$ to the following semi-linear Schr\"{o}dinger equations $$ -\Delta u+\lambda u=f(u), \quad\text{in}~\mathbb{R}^2, $$ satisfying the mass c
Externí odkaz:
http://arxiv.org/abs/2407.10258
This paper deals with the following equation $$-\Delta u =K(|x'|, x'')\Big(|x|^{-\alpha}\ast (K(|x'|, x'')|u|^{2^{\ast}_{\alpha}})\Big) |u|^{2^{\ast}_{\alpha}-2}u\quad\mbox{in}\ \mathbb{R}^N,$$ where $N\geq5$, $\alpha>5-\frac{6}{N-2}$, $2^{\ast}_{\al
Externí odkaz:
http://arxiv.org/abs/2402.04974
We study the existence of positive solutions for nonlocal systems in gradient form and set in the whole $\mathbb R^N$. A quasilinear fractional Schr\"odinger equation, where the leading operator is the $\frac Ns$-fractional Laplacian, is coupled with
Externí odkaz:
http://arxiv.org/abs/2311.13424
Autor:
Cassani, Daniele, Miyasita, Tosiya
We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first study qualitative properties of the solution to the stationary problem.
Externí odkaz:
http://arxiv.org/abs/2306.02509
We study the nonlinear Schr\"odinger equation for the $s-$fractional $p-$Laplacian strongly coupled with the Poisson equation in dimension two and with $p=\frac2s$, which is the limiting case for the embedding of the fractional Sobolev space $W^{s,p}
Externí odkaz:
http://arxiv.org/abs/2305.15274
In this paper we study the following nonlinear Choquard equation $$ -\Delta u+u=\left(\ln\frac{1}{|x|}\ast F(u)\right)f(u),\quad\text{ in }\,\mathbb{R}^2, $$ where $f\in C^1(\mathbb{R})$ and $F$ is the primitive of the nonlinearity $f$ vanishing at z
Externí odkaz:
http://arxiv.org/abs/2305.10905
Autor:
Cassani, Daniele, Du, Lele
We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings \begin{align*} W_{0}^{s,p}\left(\Omega\right)\hookrightarrow L^{q}\left(\Omega\right), \end{align*} where $N\geq1$, $0
Externí odkaz:
http://arxiv.org/abs/2305.09486
In this paper, we introduce a mathematical method to extract similarities between paintings and musical tracks. Our approach is based on the digitalization of both paintings and musical tracks by means of finite expansions in terms of orthogonal basi
Externí odkaz:
http://arxiv.org/abs/2206.14142
We consider the $N$-Laplacian Schr\"odinger equation strongly coupled with higher order fractional Poisson's equations. When the order of the Riesz potential $\alpha$ is equal to the Euclidean dimension $N$, and thus it is a logarithm, the system tur
Externí odkaz:
http://arxiv.org/abs/2201.00159
Autor:
Cassani Daniele, Du Lele
Publikováno v:
Advances in Nonlinear Analysis, Vol 12, Iss 1, Pp 683-773 (2023)
We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W0s,p(Ω)↪Lq(Ω),{W}_{0}^{s,p}(\Omega )\hspace{0.33em}\hookrightarrow \hspace{0.33em}{L}^{q}(\Omega ), where N≥1N\ge 1, 02sN\gt 2s, and the so-called Sob
Externí odkaz:
https://doaj.org/article/faa884437bfd4e49b28efccf1571e823
