A class of elliptic equations in anisotropic spaces |
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Authors: | Lucas C F Ferreira Everaldo S Medeiros Marcelo Montenegro |
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Institution: | 1. IMECC-Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, CEP 13083-859, Brazil 2. Departamento de Matemática, Universidade Federal da Paraíba, Jo?o Pessoa, PB, CEP 58051-900, Brazil
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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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