We study the global behavior of finite energy solutions to the d-dimensional focusing
nonlinear Schrödinger (NLS) equation, i∂ tu+ Δu+| u| p− 1 u= 0, with initial data. The …

We study the focusing nonlinear Schrödinger equation i\partial_t u+ Δ u+| u|^ p-1 u= 0 i∂
tu+ Δ u+| u| p-1 u= 0, x ∈ R^ N x∈ RN in the L 2-supercritical regime with finite energy and …

The blowup is studied for the nonlinear Schr\"{o} dinger equation $ iu_ {t}+\Delta u+| u|^{p-1}
u= 0$ with $ p $ is odd and $ p\ge 1+\frac 4 {N-2} $(the energy-critical or energy-supercritical …

We consider the fractional Hartree equation in the L 2-supercritical case, and find a sharp
threshold of the scattering versus blow-up dichotomy for radial data: If M [u 0] s− scsc E [u …

We consider the L 2-supercritical nonlinear Schrödinger equation with a repulsive Dirac
delta potential in one dimensional space. In a previous work, we clarified the global …

In this paper, we prove that there exists some small ε∗> 0 such that the derivative nonlinear
Schrödinger equation (DNLS) is globally well-posed in the energy space, provided that the …

Global dynamics below the standing waves for the focusing semilinear Schrödinger equation with
a repulsive Dirac delta potentia Page 1 ANALYSIS & PDE msp Volume 10 No. 2 2017 MASAHIRO …

In this work, we consider the following focusing inhomogeneous nonlinear Schrödinger
equation i∂ t u+ Δ u+| x|− b| u| pu= 0,(t, x)∈ R× RN with 0< b< min {2, N} and 4− 2 b N< p< …

We establish blow-up results for systems of NLS equations with quadratic interaction in
anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical …

There is considerable interest in nanostructured materials with interdigitated electrodes
(IDEs) platforms to detect and monitor the level of various ions in numerous applications …