Abstract
We obtain existence, nonexistence and asymptotic results for solutions to cylindrical equations of the form: \[ -\triangle u+\frac{A}{\left| y\right| ^{\alpha }}u= f\left( u\right) ~\textrm{in }\mathbb{R}^{N},~ x=\left( y,z\right) \in \mathbb{R}^{k}\times \mathbb{R}^{N-k},~N>k\geq 2, \] where $A,\alpha>0$ and $f$ is continuous and satisfies power-type growth conditions.
Citation
Marino Badiale. Michela Guida. Sergio Rolando. "Elliptic equations with decaying cylindrical potentials and power-type nonlinearities." Adv. Differential Equations 12 (12) 1321 - 1362, 2007. https://doi.org/10.57262/ade/1355867405
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