Related papers: Multi-bubble solutions for the Brezis-Nirenberg pr…
We investigate the existence of blowing-up solutions of the following almost critical problem $$ -\Delta u +V(x)u =u^{p-\e},\quad u>0\quad\mbox{in}\quad \O,\quad u=0\quad\mbox{on}\quad \partial\O, $$ where $\O$ is a bounded regular domain…
The aim of this paper is to study the finite space blow up of the solutions for a class of fourth order differential equations. Our results answer a conjecture in [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions…
The uniqueness and multiple existence of positive radial solutions to the Brezis-Nirenberg problem on a domain in the 3-dimensional unit sphere ${\mathbb S}^3$ \begin{equation*} \left\{ \begin{aligned} \Delta_{{\mathbb S}^3}U -\lambda U +…
We characterize the critical points of the double bubble problem in $\mathbb{R}^n$ and the triple bubble problem in $\mathbb{R}^3$, in the case the bubbles are convex.
We are concerned with the existence of blowing-up solutions to the following boundary value problem $$-\Delta u= \la a(x) e^u-4\pi N \delta_0\;\hbox{ in } \Omega,\quad u=0 \;\hbox{ on }\partial \Omega,$$ where $\Omega$ is a smooth and…
In this paper, we partially settle down the long standing open problem of the finite time blow-up property about the nonlinear Schr$\ddot{o}$dinger equations on some Riemannian manifolds like the standard 2-sphere $S^2$ and the hyperbolic…
We prove some results on the existence and compactness of solutions of a fractional Nirenberg problem.
We find explicit solutions to both the Oldroyd-B model with infinite Weissenberg number and the coupled Navier-Stokes/Phase-Field system. The solutions blow up in finite time.
We prove that for a symmetric, strictly log-convex density on the real line, there are four possible types of perimeter-minimizing triple bubbles. This extends the work of Bongiovanni et al., which shows that there are two possible types of…
The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data are posed in the energy space. The aim of the paper is to…
Existence of open string field theory solutions describing configurations of multiple space-filling D-branes has been a subject of numerous speculations for quite some time. In this talk we present some new results giving further support to…
We study the existence of solutions with multiple concentration to the following boundary value problem $$-\Delta u=\e^2 e^u-4\pi \sum_{p\in Z}\alpha_p \delta_{p}\;\hbox{in} \Omega,\quad u=0 \;\hbox{on}\partial \Omega,$$ where $\Omega$ is a…
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a…
Under certain conditions some solutions to five-dimensional heterotic M-theory can be accurately described by the four-dimensional action of the theory - they have a four-dimensional limit. We consider the connection between solutions of…
We are concerned with the Sinh-Gordon equation in bounded domains. We construct blow up solutions with residual mass exhibiting either partial or asymmetric blow up, i.e. where both the positive and negative part of the solution blow up.…
In this work we study the existence of nodal solutions for the problem $$ -\Delta u = \lambda u e^{u^2+|u|^p} \text{ in }\Omega, \; u = 0 \text{ on }\partial \Omega, $$ where $\Omega\subseteq \mathbb R^2$ is a bounded smooth domain and…
We introduce the super-Toda system on Riemann surfaces and study the blow-up analysis for a sequence of solutions to the super-Toda system on a closed Riemann surface with uniformly bounded energy. In particular, we show the energy…
Solution of the scattering problem turns to be very difficult task both from the formal as well as from the computational point of view. If the last two decades have witnessed decisive progress in ab initio bound state calculations,…
In this paper, we consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian \begin{equation*} \left\{\aligned &(-\Delta)^su=|u|^{p-1-\varepsilon}u\ \ \mbox{in}\ \Omega &u=0\…
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schr\"odinger equation in infinite time in dimension $N\geq 13$. Our solution is radially symmetric and converges asymptotically to the sum of two…