Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nontrival solution for nonlinear p(x)-Laplacian Dirichlet problem with
  the sign-changing weight   In this paper we study the nonlinear elliptic problem involving
p(x)-Laplacian with nonsmooth potential, where the weighted function may change
sign. By using critical point theory for locally Lipschitz functionals due to
Chang, we obtain conditions which ensure the existence of a solution for our
problem.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat