In this work we obtain a Liouville theorem for positive, bounded solutions of the equation
$\begin{align} (-\Delta)^s u= h(x_N)f(u) \hbox{in }\mathbb{R}^{N}\end{align}$
where $(-\Delta)^s$ stands for the fractional Laplacian with $s∈ (0, 1)$ , and the functions $h$ and $f$ are nondecreasing. The main feature is that the function $h$ changes sign in $\mathbb R$ , therefore the problem is sometimes termed as indefinite. As an application we obtain a priori bounds for positive solutions of some boundary value problems, which give existence of such solutions by means of bifurcation methods.
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