Concentration of positive solutions for critical quasilinear Schrödinger equation with competing potentials

References

• Kurihura S. Large-amplitude quasi-solitons in superfluid films. J Phys Soc Japan. 1981;50:3262–3267. doi: 10.1143/JPSJ.50.3262
   Google Scholar
• Liu J, Wang Y, Wang ZQ. Solutions for quasilinear Schrödinger equation via nehari method. Commun Partial Differ Equ. 2014;29:879–901. doi: 10.1081/PDE-120037335
   Google Scholar
• Liu J, Wang Y, Wang ZQ. Soliton solutions for quasilinear Schrödinger equation, II. J Differ Equ. 2003;187:473–493. doi: 10.1016/S0022-0396(02)00064-5
   Web of Science ®Google Scholar
• Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equation: a dual approach. Nonlinear Anal. 2004;56:213–226. doi: 10.1016/j.na.2003.09.008
   Web of Science ®Google Scholar
• Shen Y, Wang Y. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Anal. 2013;80:194–201. doi: 10.1016/j.na.2012.10.005
   Web of Science ®Google Scholar
• Liu X, Liu J, Wang ZQ. Quasilinear elliptic equations via perturbation method. Proc Amer Math Soc. 2013;141:253–263. doi: 10.1090/S0002-9939-2012-11293-6
   Web of Science ®Google Scholar
• Silva E, Vieira G. Quasilinear asymptotically periodic Schrödinger equations with critical growth. Calc Var Partial Differ Equ. 2010;39:1–33. doi: 10.1007/s00526-009-0299-1
   Web of Science ®Google Scholar
• Guo Y, Tang Z. Multi-bump bound state solutions for the quasilinear Schrödinger equations with critical frequency. Pac J Math. 2014;270:49–77. doi: 10.2140/pjm.2014.270.49
   Web of Science ®Google Scholar
• Liu S, Zhou J. Standing waves for quasilinear Schrödinger equations with indefinite potentials. J Differ Equ. 2018;265:3970–3987. doi: 10.1016/j.jde.2018.05.024
   Web of Science ®Google Scholar
• Xu L, Chen H. Ground state solutions for quasilinear Schrödinger equation via pohozaev manifold in Orlicz space. J Differ Equ. 2018;265:4417–4441. doi: 10.1016/j.jde.2018.06.009
   Web of Science ®Google Scholar
• Wang Y, Zou W. Bound states to critical quasilinear Schrödinger equations. NoDEA Nonlinear Differ Equ Appl. 2012;19:19–47. doi: 10.1007/s00030-011-0116-3
   Web of Science ®Google Scholar
• Wang W, Yang X, Zhao F. Existence and concentration of ground state to a quasilinear problem with competing potentials. Nonlinear Anal. 2014;102:120–132. doi: 10.1016/j.na.2014.01.025
   Web of Science ®Google Scholar
• Li Z, Zhang Y. Solutions for a class of quasilinear Schrödinger equations with critical Sobolev exponents. J Math Phys. 2017;58:1–15.
   Web of Science ®Google Scholar
• Guo Y, Tang Z. Ground state solutions for the quasilinear Schrödinger equations. Nonlinear Anal. 2012;75:3235–3248. doi: 10.1016/j.na.2011.12.024
   Web of Science ®Google Scholar
• Do Ó J, Miyagaki O, Soares S. Soliton solutions for quasilinear Schrödinger equations with critical growth. J Differ Equ. 2010;248:722–744. doi: 10.1016/j.jde.2009.11.030
   Web of Science ®Google Scholar
• Liang S, Zhang J. Existence of multi-bump solutions for a class of quasilinear Schrödinger equations in Rn involving critical growth. Milan J Math. 2015;83:55–90. doi: 10.1007/s00032-015-0236-z
   Web of Science ®Google Scholar
• Wu K. Positive solutions of quasilinear Schrödinger equations critical growth. Appl Math Lett. 2015;45:52–57. doi: 10.1016/j.aml.2015.01.005
   Web of Science ®Google Scholar
• Deng Y, Peng S, Yan S. Positive solition solutions for generalized quasilinear Schrödinger equations with critical growth. J Differ Equ. 2017;37:253–263.
   Google Scholar
• Wang Y, Zhang Y, Shen Y. Multiple solutions for quasilinear Schrödinger equations involving critical exponent. Appl Math Comput. 2010;216:849–856.
   Web of Science ®Google Scholar
• He Y, Li G. Concentrating solition solutions for quasilinear Schrödinger equations involving critical Sobolev exponents. Discrete Contin Dyn Syst. 2016;36:731–762. doi: 10.3934/dcds.2016037
   Web of Science ®Google Scholar
• Yang M. Concentrtion of positive ground state solutions for Schrödinger-maxwell systems with critical growth. Adv Nonlinear Stud. 2016;16:389–408. doi: 10.1515/ans-2015-5047
   Web of Science ®Google Scholar
• Do Ó J, Severo U. Quasiliear Schrödinger equation involving concave and convex nonlinearities. Commun Pure Appl Anal. 2009;8:621–644.
   Web of Science ®Google Scholar
• He X, Qian A, Zou W. Existence and concentration of positive solutions for quasilinear Schrödinger equations with critical growth. Nonlinearity. 2013;26:3137–3168. doi: 10.1088/0951-7715/26/12/3137
   Web of Science ®Google Scholar
• Willem M. Minimax theorem. Boston: Birkhäuser; 1996.
   Google Scholar