Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free vibrations in a wave equation modeling MEMS   We study a nonlinear wave equation appearing as a model for a membrane
(without viscous effects) under the presence of an electrostatic potential with
strength $\lambda$. The membrane has a unique stable branch of steady states
$u_{\lambda}$ for $\lambda\in\lbrack0,\lambda_{\ast}]$. We prove that the
branch $u_{\lambda}$ has an infinite number of branches of periodic solutions
(free vibrations) bifurcating when the parameter $\lambda$ is varied.
Furthermore, using a functional setting, we compute numerically the branch
$u_{\lambda}$ and their branches of periodic solutions. This approach is useful
to validate rigorously the steady states $u_{\lambda}$ at the critical value
$\lambda_{\ast}$.

19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci