Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Hamiltonian systems with critical exponential growth   In this paper, we study the following nonlocal nonautonomous Hamiltonian
system on whole $\mathbb R$ $$ \left\{\begin{array}{ll} (-\Delta)^\frac12~ u
+u=Q(x) g(v)&\quad\mbox{in } \mathbb R,\\ (-\Delta)^\frac12~ v+v =
P(x)f(u)&\quad\mbox{in } \mathbb R, \end{array}\right. $$ where
$(-\Delta)^\frac12$ is {the} square root Laplacian operator. We assume that the
nonlinearities $f, g$ have critical growth at $+\infty$ in the sense of
Trudinger-Moser inequality and the nonnegative weights $P(x)$ and $Q(x)$ vanish
at $+\infty$. Using suitable variational method combined with {the} generalized
linking theorem, we obtain the existence of {at least one} positive solution
for the above system.

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The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
16
The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: dg-ga