Ground solutions for critical quasilinear elliptic equations via Pohožaev manifold method

References

• Esteban JR , Vazquez JL . On the equation of turbulent filtration in one dimensional porous media. Nonlinear Anal. 1986;10:1303–1325.
   Web of Science ®Google Scholar
• Arcoya D , Diaz L , Tello L . S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology. J Differ Equ. 1998;150:215–225.
   Web of Science ®Google Scholar
• Drábek P , Huang Y . Multiplicity of positive solutions for some quasilinear elliptic equation in R N with critical Sobolev exponent. J Differ Equ. 1997;140:106–132.
   Web of Science ®Google Scholar
• Silva EAB , Soares SHM . Quasilinear Direchlet problems in R N with critical growth. Nonlinear Anal. 2001;43:1–20.
   Web of Science ®Google Scholar
• Lins HF , Silva SAB . Quasilinear asymptotically periodic elliptic equations with critical growth. Nonlinear Anal. 2009;71:2890–2905.
   Web of Science ®Google Scholar
• Damascelli L , Pacella F , Ramaswamy M . Symmetry of ground states of p-laplace equations via the moving plane method. Arch Ration Mech Anal. 1999;148:291–308.
   Web of Science ®Google Scholar
• do O JM , Medeiros ES . Remarks on Least energy solutions for quasilinear elliptic problem in R N . Electron J Differ Equ. 2003;83:1–14.
   Google Scholar
• Li Y , Wang Z , Zeng J . Ground states of nonlinear Schrödinger equations with potentials. Ann Inst H Poincaré Anal Non Linéaire. 2006;23:829–837.
   Web of Science ®Google Scholar
• Alves CO . Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian. Nonlinear Anal. 2002;51:1187–1206.
   Web of Science ®Google Scholar
• Liu J , Liu X , Guo Y . On an asymptotically p-linear p-Laplacian equation in R N . Nonlinear Anal. 2011;74:676–688.
   Web of Science ®Google Scholar
• Zhang Q . Ground state solution for quasilinear elliptic equation with critical growth in R N . Nonlinear Anal. 2012;75:3178–3187.
   Web of Science ®Google Scholar
• Liu S . On ground states of superlinear p-Laplacian equations in R N . J Math Anal Appl. 2010;361:48–58.
   Web of Science ®Google Scholar
• Lions PL . The concentration–compactness principle in the calculus of variations. The limit case. Part 1, 2. Rev Mat Iberoam. 1985;1:145–201.
   Google Scholar
• Zhang J . On ground state solutions for quasilinear elliptic equations with a general nonlinearity in the critical growth. J Math Anal Appl. 2013;401:232–241.
   Web of Science ®Google Scholar
• Zhao L , Zhao F . On the existence of solutions for the Schrödinger–Poisson equations. J Math Anal Appl. 2008;346:155–169.
   Web of Science ®Google Scholar
• Li G , Ye H . Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R 3 . J Differ Equ. 2014;257:566–600.
   Web of Science ®Google Scholar
• Liu Z , Guo S . On ground state solutions for the Schrödinger–Poisson equations with critical growth. J Math Anal Appl. 2014;412:435–448.
   Web of Science ®Google Scholar
• Jeanjean L . On the existence of bounded Palais–Smale sequence and application to a Landesman-Lazer type problem set on R 3 . Proc Roy Soc Edinburgh Sec A. 1999;129:787–809.
   Google Scholar
• de Figueiredo DG , Lions P-L , Nussbaum RD . A priori estimates and existence of positive solutions of semilinear elliptic equations. J Math Pures Appl. 1982;61:41–63.
   Web of Science ®Google Scholar
• Lions P . The concentration compactness principle in the calculus of variations: the locally compact case. Part 1. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:109–145; Lions P . The concentration compactness principle in the calculus of variations: the locally compact case. Part 2. Ann Inst H Poincaré Anal Non Linéaire. 1984;2:223–283.
   Web of Science ®Google Scholar
• Willem M . Minimax theorems. Boston: Birkhäuser; 1996.
   Google Scholar
• Teng K . Existence of ground state solutions for the nonlinear fractional Schrödinger–Poisson system with critical Sobolev exponent. J Differ Equ. 2016;261:3061–3106.
   Web of Science ®Google Scholar
• Ruiz D . The Schrödinger–Poisson equation under the effect of a nonlinear local term. J Funct Anal. 2006;237:655–674.
   Web of Science ®Google Scholar
• Gilbarg D , Trudinger N . Elliptic partial differential equations of second order. 2nd ed. Berlin: Springer; 1983. (Grundlehren der mathematischen Wissenschaften; vol. 224).
   Google Scholar