Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp non-existence results of prescribed L^2-norm solutions for some
  class of Schr\"odinger-Poisson and quasilinear equations   In this paper we study the existence of minimizers for $$ F(u) =
\1/2\int_{\R^3} |\nabla u|^2 dx + 1/4\int_{\R^3}\int_{\R^3}\frac{| u(x) |^2|
u(y) |^2}{| x-y |}dxdy-\frac{1}{p}\int_{\R^3}| u |^p dx$$ on the constraint
$$S(c) = \{u \in H^1(\R^3) : \int_{\R^3}|u|^2 dx = c \},$$ where $c>0$ is a
given parameter. In the range $p \in [3, 10/3]$ we explicit a threshold value
of $c>0$ separating existence and non-existence of minimizers. We also derive a
non-existence result of critical points of $F(u)$ restricted to $S(c)$ when
$c>0$ is sufficiently small. Finally, as a byproduct of our approaches, we
extend some results of \cite{CJS} where a constrained minimization problem,
associated to a quasilinear equation, is considered.

4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph