@Article{Isernia2020,
author = "Isernia, Teresa",
title = "Fractional p&q-Laplacian problems with potentials vanishing at infinity",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "1",
pages = "93--110",
doi = "https://doi.org/10.7494/OpMath.2020.40.1.93",
url = "https://doi.org/10.7494/OpMath.2020.40.1.93",
abstract = "In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional \(p\&q\)-Laplacian problems \[\begin{aligned} (-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u + V(x) (|u|^{p-2}u + |u|^{q-2}u)= K(x) f(u) \quad \text{ in } \mathbb{R}^{N},\end{aligned}\] where \(s\in (0, 1)\), \(1\lt p\lt q \lt\frac{N}{s}\), \(V: \mathbb{R}^{N}\to \mathbb{R}\) and \(K: \mathbb{R}^{N}\to \mathbb{R}\) are continuous, positive functions, allowed for vanishing behavior at infinity, \(f\) is a continuous function with quasicritical growth and the leading operator \((-\Delta)^{s}_{t}\), with \(t\in \{p,q\}\), is the fractional \(t\)-Laplacian operator.",
keywords = "fractional \(p\&q\)-Laplacian, vanishing potentials, ground state solution",
issn = "1232-9274"
}