TY  - JOUR
ID  - Isernia2020
LB  - Isernia2020
AU  - Isernia, Teresa
TI  - Fractional p&q-Laplacian problems with potentials vanishing at infinity
ST  - Fractional p&q-Laplacian problems with potentials vanishing at infinity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 1
SP  - 93
EP  - 110
DO  - https://doi.org/10.7494/OpMath.2020.40.1.93
UR  - https://doi.org/10.7494/OpMath.2020.40.1.93
AB  - 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.
KW  - fractional \(p\&q\)-Laplacian
KW  - vanishing potentials
KW  - ground state solution
SN  - 1232-9274
ER  -