Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lyapunov-Type Inequalities for Third Order Nonlinear Equations   We derive Lyapunov-type inequalities for general third order nonlinear
equations involving multiple $\psi$-Laplacian operators of the form
\begin{equation*} (\psi_{2}((\psi_{1}(u'))'))' + q(x)f(u) = 0, \end{equation*}
where $\psi_{2}$ and $\psi_{1}$ are odd, increasing functions, $\psi_{2}$ is
super-multiplicative, $\psi_{1}$ is sub-multiplicative, and
$\frac{1}{\psi_{1}}$ is convex, and $f$ is a continuous function which
satisfies a sign condition. Our results utilize $q_{+}$ and $q_{-}$, as opposed
to $|q|$ which appears in most results in the literature. Additionally, these
new inequalities generalize previously obtained results, and the proofs utilize
a different technique than most other works in the literature. Furthermore,
using the obtained inequalities, we obtain a constraint on the location of the
maximum of a solution, properties of oscillatory solutions, and an upper bound
for the number of zeroes.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph