We study the problem (-\epsilon\mathrm {i}\nabla+ A (x))^{2} u+ V (x) u=\epsilon^{-2}(\frac
{1}{| x|}\ast| u|^{2}) u, u\in L^{2}(\mathbb {R}^{3},\mathbb {C}),\text {\\\\}\epsilon\nabla …

In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM)
framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast …

Abstract J. Bourgain and H. Brezis have obtained in 2002 some new and surprising
estimates for systems of linear differential equations, dealing with the endpoint case L 1 of …

In this paper, we are concerned with the multiplicity of nontrivial solutions for the following
class of complex problems $$(-i\nabla-A (x))^ 2 {u}=\mu| u|^{q-2} u+| u|^{2^*-2} u\,{\rm …

In this article we consider the fractional Schrodinger-Poisson system $$\displaylines {(-
\Delta)^{s} u-\mu\frac {\Phi (x/| x|)}{| x|^{2s}} u+\lambda\phi u=| u|^{2^* _s-2} u,\quad\text …

MULTIPLE S1-ORBITS FOR THE SCHRODINGER–NEWTON SYSTEM 1. Introduction The
Schrödinger–Newton system in three-dimensional s Page 1 Differential and Integral Equations …

We study the existence of solutions for a class of nonlinear Schrödinger equations involving
a magnetic field with mixed Dirichlet-Neumann boundary conditions. We use Lusternik …

We consider the semilinear electromagnetic Schrödinger equation (-i ∇+ A (x))^ 2 u+ V (x)
u=| u|^ 2^ ∗-2 u, u ∈\, D_ A, 0^ 1, 2 (Ω, C), where Ω=(R^ m \\;{0\}) * R^ Nm with 2≤ m≤ N …

arXiv:1408.3023v1 [math.AP] 13 Aug 2014 The use of the Morse theory to estimate the number
of nontrivial solutions of a nonlin Page 1 arXiv:1408.3023v1 [math.AP] 13 Aug 2014 The use of …

The paper provides weighted Sobolev inequalities of the Caffarelli-Kohn-Nirenberg type for
functions with multi-radial symmetry. An elementary example of such inequality is the …