Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space

Details Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space

2011-06-23

arxiv.org/abs/1106.4622v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

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 Ekeland's variational principle.

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