Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground state solution of a nonlocal boundary-value problem   In this paper, we apply the method of the Nehari manifold to study the
Kirchhoff type equation \begin{equation*} -\Big(a+b\int_\Omega|\nabla
u|^2dx\Big)\Delta u=f(x,u) \end{equation*} submitted to Dirichlet boundary
conditions. Under a general $4-$superlinear condition on the nonlinearity $f$,
we prove the existence of a ground state solution; that is a nontrivial
solution which has least energy among the set of nontrivial solutions. In case
which $f$ is odd with respect to the second variable, we also obtain the
existence of infinitely many solutions. Under our assumptions the Nehari
manifold does not need to be of class $\mathcal{C}^1$.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex