Abstract
The equation Δu + V(x)u + b(x)u|u|ρ -1 + h(x) = 0 in \({\mathbb{R}^{n}}\) is studied in anisotropic Lebesgue spaces. We assume \({\frac{n-\theta}{n-2} < \rho < \infty}\) , with n ≥ 3 and 0 ≤ θ < 2, which covers the supercritical range. Our approach relies on estimates of the Riesz potential and allows us to consider a wide class of potentials V, including anisotropic ones. The symmetry and antisymmetry of the solutions are also addressed.
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Ferreira, L.C.F., Medeiros, E.S. & Montenegro, M. A class of elliptic equations in anisotropic spaces. Annali di Matematica 192, 539–552 (2013). https://doi.org/10.1007/s10231-011-0236-8
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DOI: https://doi.org/10.1007/s10231-011-0236-8