Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A limit equation and bifurcation diagrams of semilinear elliptic
  equations with general supercritical growth   We study radial solutions of the semilinear elliptic equation $\Delta
u+f(u)=0$ under rather general growth conditions on $f$. We construct a radial
singular solution and study the intersection number between the singular
solution and a regular solution. An application to bifurcation problems of
elliptic Dirichlet problems is given. To this end, we derive a certain limit
equation from the original equation at infinity, using a generalized similarity
transformation. Through a generalized Cole-Hopf transformation, all the limit
equations can be reduced into two typical cases, i.e., $\Delta u+u^p=0$ and
$\Delta u+e^u=0$.

36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci