Figueiredo, Giovany; Montenegro, Marcelo Fast decaying ground states for elliptic equations with exponential nonlinearity. (English) Zbl 1455.35101 Appl. Math. Lett. 112, Article ID 106779, 8 p. (2021). 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. Reviewer: Luis Filipe Pinheiro de Castro (Aveiro) Cited in 1 Document MSC: 35J61 Semilinear elliptic equations 35B33 Critical exponents in context of PDEs 35B09 Positive solutions to PDEs 35J20 Variational methods for second-order elliptic equations Keywords:critical exponential growth; subcritical equation; self-similar solution; ground state; positive solution PDFBibTeX XMLCite \textit{G. Figueiredo} and \textit{M. Montenegro}, Appl. Math. Lett. 112, Article ID 106779, 8 p. (2021; Zbl 1455.35101) Full Text: DOI References: [1] Atkinson, F. V.; Peletier, L. A., Sur les solutions radiales de l’équation \(\Delta u + \frac{ 12}{ x} \nabla u + \lambda u + | u |^{p - 1} u = 0\), C. R. Acad. Sci. Paris I, 302, 99-101 (1986) · Zbl 0606.35025 [2] Escobedo, M.; Kavian, O., Variational problems related to self-similar solutions of the heat equation, Nonlinear Anal., 11, 1103-1133 (1987) · Zbl 0639.35038 [3] Herraiz, L., Asymptotic behavior of solutions of some semilinear parabolic problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 16, 49-105 (1999) · Zbl 0918.35025 [4] Naito, Y.; Suzuki, T., Radial symmetry of self-similar solutions for semilinear heat equation, J. Differential Equations, 163, 407-428 (2000) · Zbl 0952.35044 [5] Catrina, F.; Furtado, M.; Montenegro, M., Positive solutions for nonlinear elliptic equations with fast increasing weights, Proc. R. Soc. Edinburgh A, 137, 1157-1178 (2007) · Zbl 1136.35029 [6] Furtado, M. F.; Miyagaki, O. H.; da Silva, J. P., On a class of nonlinear elliptic equations with fast increasing weight and critical growth, J. Differential Equations, 249, 1035-1055 (2010) · Zbl 1193.35044 [7] Furtado, M. F.; Medeiros, E. S.; Severo, U. B., A Trudinger-Moser inequality in a weighted Sobolev space and applications, Math. Nachr., 287, 1255-1273 (2014) · Zbl 1303.35022 [8] de Freitas, L. R.; Santos, J. A.; Severo, U. B., Quasilinear equations involving indefnite nonlinearities and exponential critical growth in \(\mathbb{R}^N\), Ann. Mat. Pura Appl. (2020), in press [9] Kavian, O., Introduction à la théorie des points critiques (1991), Springer-Verlag This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.