Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of Non-linear Lower Order Terms in Quasilinear Equations
  Involving the $p(x)$-Laplacian   In this work, we study the existence of $W_0^{1, p(\cdot)}$-solutions to the
following boundary value problem involving the $p(\cdot)$-Laplacian operator:
  \begin{equation*}
  \left\lbrace
  \begin{array}{l}
  -\Delta_{p(x)}u+|\nabla u|^{q(x)}=\lambda g(x)u^{\eta(x)}+f(x),
\quad\textnormal{ in } \Omega, \\\qquad \,\,\,\,\,\quad \quad\qquad\quad u\geq
0, \quad\textnormal{ in } \Omega
  \qquad \,\,\,\,\,\quad \quad\qquad\quad u= 0, \,\,\quad \text{on }
\partial\Omega.
  \end{array}
  \right. \end{equation*}under appropriate ranges on the variable exponents. We
give assumptions on $f$ and $g$ in terms of the growth exponents $q$ and $\eta$
under which the above problem has a non-negative solution for all $\lambda >
0$.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: solv-int