Fast decaying ground states for elliptic equations with exponential nonlinearity
For superlinear continuous functions \(f\), with exponential subcritical or exponential critical growth, the authors use a Trudinger-Moser inequality and lemmas involving the Nehari manifold, to propose conditions under which \[-\operatorname{div}(\exp(|x|^2/4) \nabla u) = \exp(|x|^2/4) f(u) \quad \mbox{in}\quad \mathbb{R}^2\] has a positive minimal energy solution.
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