Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unilateral global bifurcation for fourth-order eigenvalue problems with
  sign-changing weight   In this paper, we shall establish the unilateral global bifurcation result
for a class of fourth-order eigenvalue problems with sign-changing weight.
Under some natural hypotheses on perturbation function, we show that
$(\mu_k^\nu,0)$ is a bifurcation point of the above problems and there are two
distinct unbounded continua, $(\mathcal{C}_{k}^\nu)^+$ and
$(\mathcal{C}_{k}^\nu)^-$, consisting of the bifurcation branch
$\mathcal{C}_{k}^\nu$ from $(\mu_k^\nu, 0)$, where $\mu_k^\nu$ is the $k$-th
positive or negative eigenvalue of the linear problem corresponding to the
above problems, $\nu\in{+,-}$. As the applications of the above result, we
study the existence of nodal solutions for a class of fourth-order eigenvalue
problems with sign-changing weight. Moreover, we also establish the Sturm type
comparison theorem for fourth-order problems with sign-changing weight.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol