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• W2012599030 abstract "In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The nonlinearity of the equation is assumed to have exponential growth or have critical growth in view of Trudinger–Moser type inequality. Under some assumptions on the potential and the nonlinearity, it is proved that there is a nontrivial positive weak solution to this equation. Also it is shown that there are two distinct positive weak solutions to a perturbation of the equation. The method of proving these results is combining Trudinger–Moser type inequality, Mountain-pass theorem and Ekelandʼs variational principle." @default.
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• W2012599030 date "2012-02-01" @default.
• W2012599030 modified "2023-10-01" @default.
• W2012599030 title "Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space" @default.
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• W2012599030 doi "https://doi.org/10.1016/j.jfa.2011.11.018" @default.
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