Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: N-Laplacian equations in $\mathbb{R}^{N}$ with subcritical and critical
  growth without the Ambrosetti-Rabinowitz condition   Let $\Omega$ be a bounded domain in $\mathbb{R}^N$. In this paper, we
consider the following nonlinear elliptic equation of $N$-Laplacian type:
$-\Delta_{N}u=f(x,u)$ where $u\in W_{0}^{1,2}\{0}$ when $f$ is of subcritical
or critical exponential growth. This nonlinearity is motivated by the
Moser-Trudinger inequality. In fact, we will prove the existence of a
nontrivial nonnegative solution to the above equation without the
Ambrosetti-Rabinowitz $(AR)$ condition. Earlier works in the literature on the
existence of nontrivial solutions to $N-$Laplacian in $\mathbb{R}^{N}$ when the
nonlinear term $f$ has the exponential growth only deal with the case when $f$
satisfies the $(AR)$ condition. Our approach is based on a suitable version of
the Mountain Pass Theorem introduced by G. Cerami \cite{Ce1, Ce2}. This
approach can also be used to yield an existence result for the $p$-Laplacian
equation ($1<p<N$) in the subcritical polynomial growth case.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph