Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 2
126
Views
3
CrossRef citations to date
0
Altmetric
Articles

Multiple positive solutions for a kind of singular Schrödinger–Poisson system

Pages 270-284 | Received 31 Jan 2018, Accepted 14 May 2018, Published online: 09 Jul 2018

References

  • Alves C. Schrödinger–Poisson equations without Ambrosetti–Rabinowitz condition. J Math Anal Appl. 2011;377(2):584–592. doi: 10.1016/j.jmaa.2010.11.031
  • Ambrosetti A, Rruiz D. Multiple bound states for the Schrödinger–Poisson problem. Commun Contem Math. 2008;10(10):391–404. doi: 10.1142/S021919970800282X
  • Azzollini A. Concentration and compactness in nonlinear Schrödinger–Poisson system with a general nonlinearity. J Differential Equations. 2010;249(7):1746–1763. doi: 10.1016/j.jde.2010.07.007
  • Azzollini A, D'Avenia P, Pomponio A. On the Schrödinger–Maxwell equations under the effect of a general nonlinear term. Ann De Linstitut Henri Poincare Non Linear Anal. 2010;27(2):779–791. doi: 10.1016/j.anihpc.2009.11.012
  • Bellazzini J, Siciliano G. Scaling properties of functionals and existence of constrained minimizers. J Funct Anal. 2011;261(9):2486–2507. doi: 10.1016/j.jfa.2011.06.014
  • Cerami G, Vaira G. Positive solutions for some non-autonomous Schrödinger–Poisson systems. J Differ Equ. 2010;248(3):521–543. doi: 10.1016/j.jde.2009.06.017
  • Ianni I, Ruiz D. Ground and bound states for a static Schrödinger–Poisson–Slater problem. Commun Contem Math. 2012;14(1):1250003.
  • Jeanjean L, Coz SL. An existence stability result for standing waves of nonlinear Schrödinger equations. Adv Differ Equ. 2006;11(7):813–840.
  • Kikuchi H. Existence and stability of standing waves for Schrödinger–Poisson–Slater equation. Adv. Nonlinear Stud. 2007;7(3):403–437. doi: 10.1515/ans-2007-0305
  • Mugnai TDD. Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations. Proc R Soc Edinb. 2004;134(5):893–906. doi: 10.1017/S030821050000353X
  • Ruiz D. The Schrödinger–Poisson equation under the effect of a nonlinear local term. J Funct Anal. 2006;237(2):655–674. doi: 10.1016/j.jfa.2006.04.005
  • Wang J, Xu J, Zhang F, Chen X. Existence of multi-bump solutions for a semilinear Schrödinger–Poisson system. Nonlinearity. 2013;26(26):1377–1399. 23 doi: 10.1088/0951-7715/26/5/1377
  • Wang Z, Zhou H-S. Positive solution for a nonlinear stationary Schrödinger-Poisson system in R3. Discrete Contin Dyn Syst. 2007;18(4):121–134. doi: 10.3934/dcds.2007.18.121
  • Zhao L, Zhao F. Positive solutions for Schrödinger–Poisson equations with a critical exponent. Nonlin Anal. 2009;70(6):2150–2164. doi: 10.1016/j.na.2008.02.116
  • Azzollini A, D'Avenia P. On a system involving a critically growing nonlinearity. J Math Anal Appl. 2012;387(1):433–438. doi: 10.1016/j.jmaa.2011.09.012
  • Azzollini A, D'Avenia P, Luisi V. Generalized Schrödinger–Poisson type systems. Commun Pure Appl Anal. 2010;12(2):867–879. doi: 10.3934/cpaa.2013.12.867
  • Benci V, Fortunato D. An eigenvalue problem for Schrödinger–Maxwell equations. Topol Methods Nonlin Anal. 1998;11(2):283–293. doi: 10.12775/TMNA.1998.019
  • Zhang Q. Existence, uniqueness and multiplicity of positive solutions for Schrödinger–Poisson system with singularity. J Math Anal Appl. 2015;437(1):160–180. doi: 10.1016/j.jmaa.2015.12.061
  • Jiang Y, Zhou H. Schrödinger–Poisson system with singular potential. J Math Anal Appl. 2014;417(1):411–438. doi: 10.1016/j.jmaa.2014.03.034
  • Arcoya D, Moreno-Mérida L. Multiplicity of solutions for a Dirichlet problem with a strongly singular nonlinearity. Nonlinear Anal. 2014;95(95):281–291. doi: 10.1016/j.na.2013.09.002
  • Boccardo L. A dirichlet problem with singular and supercritical nonlinearities. Nonlin Anal. 2012;75(12):4436–4440. doi: 10.1016/j.na.2011.09.026
  • Haitao Y. Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem. J Differ Equ. 2003;189(189):487–512. doi: 10.1016/S0022-0396(02)00098-0
  • Hirano N, Saccon C, Shioji N. Brezis–Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem. J Differ Equ. 2008;245(8):1997–2037. doi: 10.1016/j.jde.2008.06.020
  • Lair AV. Classical and weak solutions of a singular semilinear elliptic problem. J Math Anal Appl. 1997;211(2):371–385. doi: 10.1006/jmaa.1997.5470
  • Sun Y, Li S. Structure of ground state solutions of singular semilinear elliptic equations. Nonlin Anal. 2003;55(4):399–417. doi: 10.1016/S0362-546X(03)00244-X
  • Sun Y, Wu S, Long Y. Combined effects of singular and superlinear nonlinearities in some singular boundary value problems. J Differ Equ. 2001;176(2):511–531. doi: 10.1006/jdeq.2000.3973
  • Wang X, Zhao L, Zhao P. Combined effects of singular and critical nonlinearities in elliptic problems. Nonlin Anal. 2013;87(4):1–10. doi: 10.1016/j.na.2013.03.019
  • Wang X, Zhao P, Zhang L. The existence and multiplicity of classical positive solutions for a singular nonlinear elliptic problem with any growth exponents. Nonlin Anal. 2014;101(101):37–46. doi: 10.1016/j.na.2014.01.016
  • Willem M. Minimax theorems progress in nonlinear differential equations and their applications.Boston MA;Birkhäuser Boston, Inc; 1996.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.