Abstract
In this paper, we prove a suitable Trudinger–Moser inequality with a singular weight in \({\mathbb{R}^N}\) and as an application of this result, using the mountain-pass theorem we establish sufficient conditions for the existence of nontrivial solutions to quasilinear elliptic partial differential equations of the form
where \({V:\mathbb{R}^N\rightarrow \mathbb{R}}\) is a continuous potential, \({a\in[0,N)}\) and \({f: \mathbb{R}^N\times\mathbb{R}\rightarrow \mathbb{R}}\) behaves like exp(α|u|N/(N-1)) when |u| → ∞.
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Research partially supported by CNPq grants 142002/2006-2.
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de Souza, M. On a singular elliptic problem involving critical growth in \({\mathbb{R}^{\bf N}}\) . Nonlinear Differ. Equ. Appl. 18, 199–215 (2011). https://doi.org/10.1007/s00030-010-0091-0
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DOI: https://doi.org/10.1007/s00030-010-0091-0