Radial ground state sign-changing solutions for asymptotically cubic or super-cubic fractional Schrödinger-Poisson systems

References

• Laskin N. Fractional Schrödinger equation. Phys Rev E. 2002;66:056108–056114. doi: 10.1103/PhysRevE.66.056108
   Web of Science ®Google Scholar
• Laskin N. Fractional quantum machanics and Lévy path integrals. Phys Lett A. 2000;268:298–305. doi: 10.1016/S0375-9601(00)00201-2
   Web of Science ®Google Scholar
• Dáavila J, del Pino M, Wei J. Concentrating standing waves for the fractional nonlinear Schrödinger equation. J Differential Equations. 2014;256:858–892. doi: 10.1016/j.jde.2013.10.006
   Web of Science ®Google Scholar
• Dávila J, del Pino M, Dipierro S, et al. Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum. Anal PDE. 2015;8:1165–1235. doi: 10.2140/apde.2015.8.1165
   Web of Science ®Google Scholar
• Felmer P, Quaas A, Tan JG. Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian. Proc R Soc Edinburgh Sect A. 2012;142:1237–1262. doi: 10.1017/S0308210511000746
   Web of Science ®Google Scholar
• Long W, Peng S, Yang J. Infinitely many positive solutions and sign-changing solutions for nonlinear fractional scalar field equations. Discret Contin Dynam Syst. 2016;36:917–939.
   Web of Science ®Google Scholar
• Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573. doi: 10.1016/j.bulsci.2011.12.004
   Web of Science ®Google Scholar
• Benci V, Fortunato D. An eigenvalue problem for the Schrödinger-Maxwell equations. Topol Methods Nonlinear Anal. 1998;11:283–293. doi: 10.12775/TMNA.1998.019
   Google Scholar
• D'Aprile T, Mugnai D. Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations. Proc R Soc Edinb Sect A. 2004;134:893–906. doi: 10.1017/S030821050000353X
   Google Scholar
• Mugnai D. The Schrödinger-Poisson system with positive potential. Commun Partial Differ Equ. 2011;36:1099–1117. doi: 10.1080/03605302.2011.558551
   Web of Science ®Google Scholar
• Vaira G. Ground states for Schrödinger-Poisson type systems. Ric Mat. 2011;60:263–297. doi: 10.1007/s11587-011-0109-x
   Google Scholar
• Alves CO, Souto MAS, Soares SM. A sign-changing solution for the Schrödinger-Poisson equation. Rocky Mt J Math. 2017;47:1–25. doi: 10.1216/RMJ-2017-47-1-1
   Web of Science ®Google Scholar
• Ambrosetti A, Ruiz D. Multiple bound states for the Schrödinger-Poisson problem. Commun Contemp Math. 2008;10:391–404. doi: 10.1142/S021919970800282X
   Web of Science ®Google Scholar
• Cerami G, Vaira G. Positive solutions for some non-autonomous Schrödinger-Poisson systems. J Differential Equations. 2010;248:521–543. doi: 10.1016/j.jde.2009.06.017
   Web of Science ®Google Scholar
• D'Aprile T, Wei J. On bound states concentrating on spheres for the Maxwell-Schrödinger equation. SIAM J Math Anal. 2005;37:321–342. doi: 10.1137/S0036141004442793
   Web of Science ®Google Scholar
• Huang WN, Tang XH. Ground-State solutions for asymptotically cubic Schrödinger-Maxwell equations. Mediterr J Math. 2016;13:3469–3481. doi: 10.1007/s00009-016-0697-5
   Web of Science ®Google Scholar
• Huang WN, Tang XH. Semiclassical solutions for the nonlinear Schrödinger-Maxwell equations. J Math Anal Appl. 2014;415:791–802. doi: 10.1016/j.jmaa.2014.02.015
   Web of Science ®Google Scholar
• He XM, Zou WM. Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth. J Math Phys. 2012;53:023702. doi: 10.1063/1.3683156
   Web of Science ®Google Scholar
• Ruiz D. On the Schrödinger-Poisson-Slater system: behavior of minimizers, radial and nonradial cases Arch. Ration Mech Anal. 2010;198:349–368. doi: 10.1007/s00205-010-0299-5
   Web of Science ®Google Scholar
• Chen ST, Tang XH. Improved results for Klein-Gordon-Maxwell systems with general nonlinearity. Disc Contin Dyn Syst. 2018;38:2333–2348. doi: 10.3934/dcds.2018096
   Web of Science ®Google Scholar
• Chen ST, Tang XH. Ground state sign-changing solutions for a class of Schrödinger-Poisson type problems in R3. Z Angew Math Phys. 2016;67:1–18. doi: 10.1007/s00033-015-0604-0
   Google Scholar
• Tang XH. Non-Nehari manifold method for asymptotically linear Schrödinger equation. J Aust Math Soc. 2015;98:104–116. doi: 10.1017/S144678871400041X
   Web of Science ®Google Scholar
• Tang XH. Non-Nehari manifold method for asymptotically periodic Schrödinger equation. Sci China Math. 2015;58:715–728. doi: 10.1007/s11425-014-4957-1
   Web of Science ®Google Scholar
• Tang XH, Lin X, Yu J. Nontrivial solutions for Schrödinger equation with local super-quadratic conditions. J Dyn Differ Equ. 2018;1–15. DOI:10.1007/s10884-018-9662-2.
   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
• Alves CO, Souto MAS, Soares SM. A sign-changing solution for the Schrödinger-Poisson equation. Rocky Mt J Math. 2017;47:1–25. doi: 10.1216/RMJ-2017-47-1-1
   Web of Science ®Google Scholar
• Ianni I. Sign-Changing radial solutions for the Schrödinger-Poisson-Slater problem. Topol Methods Nonlinear Anal. 2013;41:365–385.
   Web of Science ®Google Scholar
• Liang ZP, Xu J, Zhu XL. Revisit to sign-changing solutions for the nonlinear Schrödinger-Poisson system in R3. J Math Anal Appl. 2016;435:783–799. doi: 10.1016/j.jmaa.2015.10.076
   Google Scholar
• Shuai W, Wang QF. Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger-Poisson system in R3. Z Angew Math Phys. 2015;66:3267–3282. DOI:10.1007/s00033-015-0571-5. doi: 10.1007/s00033-015-0571-5
   Web of Science ®Google Scholar
• Wang ZP, Zhou HS. Sign-changing solutions for the nonlinear Schrödinger-Poisson system in R3. Calc Var Partial Differential Equations. 2015;52:927–943. doi: 10.1007/s00526-014-0738-5
   Web of Science ®Google Scholar
• Duarte RC, Souto MAS. Fractional Schrödinger-Poisson equations with general nonlinearity. 2016. arXiv preprint arXiv:1610.06623.
   Google Scholar
• Feng X. Nontrivial solution for Schrödinger-Poisson equations involving a fractional nonlocal operator via perturbation methods. Z Angew Math Phys. 2016;67:1–10. doi: 10.1007/s00033-016-0667-6
   Web of Science ®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. doi: 10.1016/j.jde.2016.05.022
   Web of Science ®Google Scholar
• Liu W. Existence of multi-bump solutions for the fractional Schrödinger-Poisson system. J Math Phys. 2016;57:779–791.
   Web of Science ®Google Scholar
• Zhang J, Squassina M. Fractional Schrödinger-Poisson systems with a general subcritical or critical nonlinearity. Adv Nonlinear Stud. 2016;16:15–30.
   Web of Science ®Google Scholar
• Chen ST, Peng JW, Tang XH. Ground state solutions for asymptotically periodic fractional Schrödinger-Poisson problems with asymptotically cubic or super-cubic nonlinearities. Math Methods Appl Sci. 2016;40:4948–4961.
   Web of Science ®Google Scholar
• Teng KM. Existence of ground state solutions for the nonlinear fractional Schrödinger-Poisson system with critical Sobolev exponent. J Differential Equations. 2016;261:3061–3106. doi: 10.1016/j.jde.2016.05.022
   Web of Science ®Google Scholar
• Miranda C. Un'osservazione su un teorema di Brouwer. Boll Unione Mat Ital. 1940;3:5–7.
   Google Scholar
• Tang XH, Cheng BT. Ground state sign-changing solutions for Kirchhoff type problems in bounded domains. J Differential Equations. 2016;261:2384–2402. doi: 10.1016/j.jde.2016.04.032
   Web of Science ®Google Scholar