References
- Pohozaev SI. The Sobolev embedding in the case pl = n. In: Proceedings of the Technical Scientific Conference on Advances of Scientific Research 1964–1965. Mathematics Section, Moscov. Energet. Inst.; 1965. p. 158–170.
- Trudinger NS. On the imbedding into Orlicz spaces and some applications. J. Math. Mech. 1967;17:473–484.
- Moser J. A sharp form of an inequality by N. Trudinger. Indiana Univ. Math. J. 1971;20:1077–1092.
- Hempel JA, Morris GR, Trudinger NS. On the sharpness of a limiting case of the Sobolev imbedding theorem. Bull. Aust. Math. Soc. 1970;3:369–373.
- Brezis H, Wainger S. A note on limiting cases of Sobolev embeddings and convolution inequalities. Commun. Partial Differ. Equ. 1980;5:773–789.
- Adimurthi. Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the n-Laplacian. Ann. Scuola norm. Sup. Pisa Cl. Sci. 1990;17:393–413.
- de Figueiredo DG, Miyagaki OH, Ruf B. Elliptic equations in ℝ2 with nonlinearities in the critical growth range. Calc. Var. Partial Differ. Equ. 1995;4:139–153.
- Adams RA. Sobolev spaces. Vol. 65, Pure and Applied Mathematics. New York: Academic Press; 1975.
- do Ó JM. N-Laplacian equations in ℝN with critical growth. Abstr. Appl. Anal. 1997;2: 301–315.
- Panda R. Nontrivial solution of a quasilinear elliptic equation with critical growth in ℝn. Proc. Indian Acad. Sci. Math. Sci. 1995;105:425–444.
- de Souza M. Existence and multiplicity of solutions for a singular semilinear elliptic problem in ℝ2. Electron. J. Differ. Equ. 2011;98:1–13.
- de Souza M, do Ó JM. On a class of singular Trudinger-Moser type inequalities and its applications. Math. Nachr. 2011;284:1754–1776.
- do Ó JM, de Medeiros ES, Severo UB. A nonhomogeneous elliptic problem involving critical growth in dimension two. J. Math. Anal. Appl. 2008;345:286–304.
- do Ó JM, de Medeiros ES, Severo UB. On a quasilinear nonhomogeneous elliptic equation with critical growth in ℝN. J. Differ. Equ. 2009;246:1363–1386.
- do Ó JM, Souto MAS. On a class of nonlinear Schrödinger equations in ℝ2 involving critical growth. J. Differ. Equ. 2001;174:289–311.
- Giacomoni J, Sreenadh K. A multiplicity result to a nonhomogeneous elliptic equation in whole space ℝ2. Adv. Math. Sci. Appl. 2005;15:467–488.
- Lam N, Lu G. Existence and multiplicity of solutions to equations of N-Laplacian type with critical exponential growth in ℝN. J. Funct. Anal. 2012;262:1132–1165.
- Yang Y. Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space. J. Funct. Anal. 2012;262:1679–1704.
- Berestycki H, Lions P-L. Nonlinear scalar field equations. I. Existence of infinitely many solutions. Arch. Ration. Mech. Anal. 1983;82:313–345.
- Berestycki H, Lions P-L. Nonlinear scalar field equations. II. Existence of a ground state. Arch. Ration. Mech. Anal. 1983;82:347–375.
- Strauss WA. Mathematical aspects of classical nonlinear field equations. (Proc. IX G.I.F.T. Internat. Sem. Theoret. Phys., Univ. Zaragoza, Jaca, 1978). Vol. 98, Lecture Notes in Physics. Springer; 1979. p. 123–149.
- Cao DM. Nontrivial solution of semilinear elliptic equation with critical exponent in ℝ2. Commun. Partial Differ. Equ. 1992;17:407–435.
- do Ó JM, Ruf B. On a Schrödinger equation with periodic potential and critical growth in ℝ2. Nonlinear Differ. Equ. Appl. 2006;13:167–192.
- Adimurthi, Yang Y. An interpolation of Hardy inequality and Trudinger–Moser inequality in ℝN and its applications. Int. Math. Res. Not. 2010;13:2394–2426.
- Brezis H. Functional analysis, Sobolev spaces and partial differential equations. Universitext. New York: Springer; 2011.
- de Figueiredo DG, do Ó JM, Ruf B. Elliptic equations and systems with critical Trudinger–Moser nonlinearities. Discrete Contin. Dyn. Syst. 2011;30:455–476.
- Candela AM, de Medeiros ES, Giuliana P, Perera K. Weak solutions of quasilinear elliptic systems via the cohomological index. Topol. Methods Nonlinear Anal. 2010;36:1–18.
- de Paiva FO, do Ó JM, de Medeiros ES. Multiplicity results for some quasilinear elliptic problems. Topol. Methods Nonlinear Anal. 2009;34:77–89.
- Ding YH, Szulkin A. Bound states for semilinear Schrödinger equations with sign-changing potential. Calc. Var. Partial Differ. Equ. 2007;29:397–419.
- Sirakov B. Standing wave solutions of the nonlinear Schrödinger equation in ℝN. Ann. Mat. Pura Appl. (4). 2002;181:73–83.
- Wang Z, Zhou HS. Ground state for nonlinear Schrödinger equation with sign-changing and vanishing potential. J. Math. Phys. 2011;52:113–704.
- Nelson E. Feynman integrals and the Schrödinger equation. J. Math. Phys. 1964;5:332–343.
- Serrin J. Local behavior of solutions of quasi-linear equations. Acta Math. 1964;111:248–302.
- Kavian O. Introduction á la théorie des points critiques et applications aux problèmes elliptiques. Paris: Springer-Verlag; 1993.
- Carl S, Heikkilä S. Elliptic problems with lack of compactness via a new fixed point theorem. J. Differ. Equ. 2002;186:122–140.