The authors prove the existence of radial solutions for the nonlinear elliptic problem −div(A(|x|)∇u) + V(|x|)u = K(|x|)f(u) in ℝN , with suitable hypotheses on the radial potentials A, V, K. They first get compact embeddings of radial weighted Sobolev spaces into sums of weighted Lebesgue spaces, and then they apply standard variational techniques to get existence results.
Radial nonlinear elliptic problems with singular or vanishing potentials
M. Badiale;ZACCAGNI, FEDERICA
2018-01-01
Abstract
The authors prove the existence of radial solutions for the nonlinear elliptic problem −div(A(|x|)∇u) + V(|x|)u = K(|x|)f(u) in ℝN , with suitable hypotheses on the radial potentials A, V, K. They first get compact embeddings of radial weighted Sobolev spaces into sums of weighted Lebesgue spaces, and then they apply standard variational techniques to get existence results.
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