Ground state solutions for Choquard equations with Hardy potentials and critical nonlinearity

References

• Reed M, Simon B. Methods of modern mathematical physics. New York (NY): Academic Press; 1978. (Analysis of operators; vol. IV).
   Google Scholar
• Frank WM, Land DJ, Spector RM. Singular potentials. Rev Mod Phys. 1971;43:36–98.
   Web of Science ®Google Scholar
• Felli V, Terracini S. Elliptic equations with multi-singular inverse-square potentials and critical nonlineaity. Commun Partial Differ Equ. 2006;31(1–3):469–495.
   Web of Science ®Google Scholar
• Garcia Azorero JP, Peral Alonso I. Hardy inequalities and some critical elliptic and parabolic problems. J Differ Equ. 1998;144:441–476.
   Web of Science ®Google Scholar
• Bahri A, Coron JM. On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain. Commun Pure Appl Math. 1988;41:253–294.
   Web of Science ®Google Scholar
• Chen S, Tang X. Improved results for Klein-Gordon-Maxwell systems with general nonlinearity. Disc Contin Dyn Syst A. 2018;38:2333–2348.
   Web of Science ®Google Scholar
• Ji C, Rădulescu VD. Multi-bump solutions for the nonlinear magnetic Schrödinger equation with exponential critical growth in R2. Manuscripta Math. 2021;164:509–542.
   Google Scholar
• Deng Y, Jin L, Peng S. Solutions of Schrödinger equations with inverse square potential and critical nonlinearity. J Differ Equ. 2012;253(5):1376–1398.
   Web of Science ®Google Scholar
• Felli V, Marchini E, Terracini S. On Schrödinger operators with multipolar inverse-square potentials. J Funct Anal. 2007;250(2):265–316.
   Web of Science ®Google Scholar
• Guo Q, Mederski J. Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials. J Differ Equ. 2016;260:4180–4202.
   Web of Science ®Google Scholar
• Liang SH, Pucci P, Zhang BL. Multiple solutions for critical Choquard–Kirchhoff type equations. Adv Nonlinear Anal. 2021;10:400–419.
   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.
   Web of Science ®Google Scholar
• Tang XH. Non-Nehari manifold method for asymptotically periodic Schrödinger equation. Sci China Math. 2015;58:715–728.
   Web of Science ®Google Scholar
• Tang X, Chen S. Ground state solutions of Nehari–Poho z˘aev type for Kirchhoff-type problems with general potentials. Calc Var Partial Differ Equ. 2017;56:110–134.
   Web of Science ®Google Scholar
• Terracini S. On positive solutions to a class equations with a singular coefficient and critical exponent. Adv Differ Equ. 1996;2:241–264.
   Google Scholar
• Abdellaoui B, Felli V, Peral I. Existence and multiplicity for perturbations of equation involving Hardy inequality and critical Sobolev exponent in the whole RN. Adv Differ Equ. 2004;9:481–508.
   Web of Science ®Google Scholar
• Felli V. On the existence of ground state solutions to nonlinear Schrödinger equations with multisingular inverse-square anisotropic potentials. J Anal Math. 2009;108:189–217.
   Web of Science ®Google Scholar
• Ruiz D, Willem M. Elliptic problems with critical exponents and Hardy potentials. J Differ Equ. 2003;190(2):524–538.
   Web of Science ®Google Scholar
• Smets D. Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans Am Math Soc. 2005;357(7):2909–2938.
   Web of Science ®Google Scholar
• Lieb EH, Loss M. Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2001.
   Google Scholar
• Moroz V, Van Schaftingen J. Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265:153–184.
   Web of Science ®Google Scholar
• Van Schaftingen J, Xia JK. Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent. J Math Anal Appl. 2018;464:1184–1202.
   Web of Science ®Google Scholar
• Li GD, Tang CL. Existence of a ground state solution for Choquard equation with the upper critical exponent. Comput Math Appl. 2018;76:2625–2647.
   Web of Science ®Google Scholar
• Li XF, Ma SW. Choquard equations with critical nonlinearities. Commun Contemp Math. 2020;22(4):1950023
   Web of Science ®Google Scholar
• Moroz V, Van Schaftingen J. Existence of groundstate for a class of nonlinear Choquard equations. Trans Am Math Soc. 2015;367(9):6557–6579.
   Web of Science ®Google Scholar
• Mattner L. Strict definiteness of integrals via complete monotonicity of derivatives. Trans Am Math Soc. 1997;349:3321–3342.
   Web of Science ®Google Scholar
• Willem M. Minimax theorems. Boston (MA): Birkhäuser Boston; 1996. (Progress in nonlinear differential equations and their applications; vol. 24).
   Google Scholar
• Luo HX. Ground state solutions of Poho z˘aev type and Nehari type for a class of nonlinear Choquard equations. J Math Anal Appl. 2018;467(2):842–862.
   Web of Science ®Google Scholar
• Jeanjean L. Existence of solutions with prescribed norm for semilinear elliptic equations. Nonlinear Anal. 1997;28(10):1633–1659.
   Web of Science ®Google Scholar
• Jeanjean L, Tanaka K. A positive solution for a nonlinear Schrödinger equation on RN. Indiana Univ Math J. 2005;54(2):443–464.
   Web of Science ®Google Scholar
• Zhang J, Zou WM. The critical case for a Berestycki-Lions theorem. Sci China Math. 2014;57(3):541–554.
   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 Equ. 2003;193:424–434.
   Web of Science ®Google Scholar