Nehari-type ground state solutions for Schrödinger equations with Hardy potential and critical nonlinearities

References

• Smets D. Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans Amer Math Soc. 2005;357:2909–2938. doi: 10.1090/S0002-9947-04-03769-9
   Web of Science ®Google Scholar
• Lions P-L. The concentration-compactness principle in the calculus of variations. The limit case. Rev Mat Ibero Americana. 1985;1:45–121. doi: 10.4171/RMI/12
   Google Scholar
• Benci V, Cerami G. Existence of positive solutions of the equation −△u+a(x)u=u(N+2)/(N−2) in RN. J Funct Anal. 1990;88(1):90–117. doi: 10.1016/0022-1236(90)90120-A
   Web of Science ®Google Scholar
• Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical exponents. Comm Pure Appl Math. 1983;36:437–477. doi: 10.1002/cpa.3160360405
   Web of Science ®Google Scholar
• Cao D, Han P. Solutions for semilinear elliptic equations with critical exponents and Hardy potential. J Differ Eq. 2004;205:521–537. doi: 10.1016/j.jde.2004.03.005
   Web of Science ®Google Scholar
• Cao D, Peng S. A global compactness result for singular elliptic problems involving critical Sobolev exponent. Proc Amer Math Soc. 2003;131:1857–1866. doi: 10.1090/S0002-9939-02-06729-1
   Web of Science ®Google Scholar
• Cao D, Peng S. A note on the sign-changing solutions to elliptic problem with critical Sobolev and Hardy terms. J Differ Eq. 2003;193:424–434. doi: 10.1016/S0022-0396(03)00118-9
   Web of Science ®Google Scholar
• Capozzi A, Fortunato D, Palmieri G. An existence result for nonlinear elliptic problems involving critical Sobolev exponent. Ann Inst H Poincaré Anal Non Lineaire. 1985;2:463–470. doi: 10.1016/S0294-1449(16)30395-X
   Web of Science ®Google Scholar
• Chabrowski J, Szulkin A. On a semilinear Schrödinger equation with critical Sobolev exponent. Proc Amer Math Soc. 2002;130:85–93. doi: 10.1090/S0002-9939-01-06143-3
   Web of Science ®Google Scholar
• Chen ST, Tang XH. Improved results for Klein-Gordon-Maxwell systems with general nonlinearity. Disc Contin Dyn Syst. - A 2018;38:2333–2348. doi: 10.3934/dcds.2018096
   Web of Science ®Google Scholar
• Chen W, Wei J, Yanc S. Infinitely many solutions for the Schrödinger equations in RN with critical growth. J Differ Eq. 2012;252:2425–2447. doi: 10.1016/j.jde.2011.09.032
   Web of Science ®Google Scholar
• Chen Y, Tang XH. Ground state solutions for p-superlinear p-Laplace equation. J Aust Math Soc. 2014;97:48–62. doi: 10.1017/S1446788714000135
   Web of Science ®Google Scholar
• Guo Q, Mederski J. Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potential. J Differ Eq. 2016;260:4180–4202. doi: 10.1016/j.jde.2015.11.006
   Web of Science ®Google Scholar
• Chen Z, Zou W. On an elliptic problem with critical exponent and Hardy potential. J Differ Eq. 2012;252:969–987. doi: 10.1016/j.jde.2011.09.042
   Web of Science ®Google Scholar
• Deng Y, Jin L, Peng S. Solutions of Schrödinger equations with inverse square potential and critical nonlinearity. J Differ Eq. 2012;253:1376–1398. doi: 10.1016/j.jde.2012.05.009
   Web of Science ®Google Scholar
• Egnell E. Elliptic boundary value problems with singular coefficients and critical nonlinearities. Indiana Univ Math J. 1989;38:235–251. doi: 10.1512/iumj.1989.38.38012
   Web of Science ®Google Scholar
• Felli V, Marchini EM, Terracini S. On Schrödinger operators with multipolar inverse-square potentials. J Funct Anal. 2007;250:265–316. doi: 10.1016/j.jfa.2006.10.019
   Web of Science ®Google Scholar
• Ferrero A, Gazzola F. Existence of solutions for singular critical growth semilinear elliptic equations. J Differ Eq. 2001;177:494–522. doi: 10.1006/jdeq.2000.3999
   Web of Science ®Google Scholar
• Garcia AJ, Peral I. Hardy inequalities and some critical and parabolic problems. J Differ Eq. 1998;144:441–476. doi: 10.1006/jdeq.1997.3375
   Web of Science ®Google Scholar
• Ghoussoub N, Yuan C. Multiple solutions for quasilinear PDEs involving critical Sobolev and Hardy exponents. Trans Amer Math Soc. 2000;352:5703–5743. doi: 10.1090/S0002-9947-00-02560-5
   Web of Science ®Google Scholar
• Ruiz D, Willem M. Elliptic problems with critical exponents and Hardy potentials. J Differ Eq. 2003;190:524–538. doi: 10.1016/S0022-0396(02)00178-X
   Web of Science ®Google Scholar
• Struwe M. A global compactness result for elliptic boundary value problems involving limiting nonlinearities. Math Z. 1984;187:511–517. doi: 10.1007/BF01174186
   Web of Science ®Google Scholar
• Szulkin A, Weth T. Ground state solutions for some indefinite variational problems. J Funct Anal. 2009;257(12):3802–3822. doi: 10.1016/j.jfa.2009.09.013
   Web of Science ®Google Scholar
• Tang XH. Infinitely many solutions for semilinear Schrödinger equations with sign-changing potential and nonlinearity. J Math Anal Appl. 2013;401:407–415. doi: 10.1016/j.jmaa.2012.12.035
   Web of Science ®Google Scholar
• Tang XH, Chen ST. Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials. Calc Var Partial Differ Equ. 2017;56:110–134. doi: 10.1007/s00526-017-1214-9
   Web of Science ®Google Scholar
• Tang XH, Lin XY. Existence of ground state solutions of Nehari-Pankov type to Schrödinger systems. Sci China Math. 2019;62. doi:10.1007/s11425-017-9332-3.
   Google Scholar
• Tang XH, Lin X, Yu JS. Nontrivial solutions for Schrödinger equation with local super-quadratic conditions. J Dyn Differ Equ. 2018;0:1–15. doi:10.1007/s10884-018-9662-2.
   Google Scholar
• Terracini S. On positive solutions to a class equations with a singular coefficient and critical exponent. Adv Differ Eq. 1996;2:241–264.
   Google Scholar
• Willem M. Minimax theorems. Boston: Birkhäuser; 1996.
   Google Scholar
• Lin XY, Tang XH. Nehari-type ground state positive solutions for superlinear asymptotically periodic Schrödinger equations. Abst Appl Anal. 2014; Article ID 607078, doi:10.1155/2014/607078.
   Google Scholar
• Gidas B, Ni WM, Nirenberg L. Symmetry of positive solutions of nonlinear elliptic equations in RN. Adv Math Suppl Stud A. 1981;7:209–243.
   Google Scholar