Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and Multiplicity for elliptic p-Laplacian problems with
  critical growth in the gradient   We consider the boundary value problem $-\Delta_p u = \lambda c(x) |u|^{p-2}u
+ \mu(x) |\grad u|^p + h(x)$, $u \in W^{1,p}_0(\Omega) \cap
L^{\infty}(\Omega)$, where $\Omega \subset \mathbb R^N$, $N \geq 2$, is a
bounded domain with smooth boundary. We assume $c$, $h \in L^q(\Omega)$ for
some $q > \max\{N/p,1\}$ with $c \gneqq 0$ and $\mu \in L^{\infty}(\Omega)$. We
prove existence and uniqueness results in the coercive case $ \lambda \leq 0$
and existence and multiplicity results in the non-coercive case $ \lambda >0$.
Also, considering stronger assumptions on the coefficients, we clarify the
structure of the set of solutions in the non-coercive case.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph