Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The bifurcation diagram of an elliptic Kirchhoff-type equation with
  respect to the stiffness of the material   We study a superlinear and subcritical Kirchhoff type equation which is
variational and depends upon a real parameter $\lambda$. The nonlocal term
forces some of the fiber maps associated with the energy functional to have two
critical points. This suggest multiplicity of solutions and indeed we show the
existence of a local minimum and a mountain pass type solution. We characterize
the first parameter $\lambda_0^*$ for which the local minimum has non-negative
energy when $\lambda\ge \lambda_0^*$. Moreover we characterize the extremal
parameter $\lambda^*$ for which if $\lambda>\lambda^*$, then the only solution
to the Kirchhoff equation is the zero function. In fact, $\lambda^*$ can be
characterized in terms of the best constant of Sobolev embeddings. We also
study the asymptotic behavior of the solutions when $\lambda\downarrow 0$.

14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org