82
Views
4
CrossRef citations to date
0
Altmetric
Review Article

Existence results for zero mass polyharmonic system

, &
Pages 1613-1629 | Received 23 Jul 2019, Accepted 04 Oct 2019, Published online: 30 Oct 2019

References

  • Bartsch T. Critical equations for the polyharmonic operator. World Scientific; 2003. 35–43.
  • Ghanmi A, Maagli H, Rădulescu V, et al. Large and bounded solutions for a class of nonlinear Schrödinger stationary systems. Anal Appl. 2009;7(4):391–404. doi: 10.1142/S0219530509001463
  • Li GB, Wang CH. Existence of nontrivial solutions to a semilinear elliptic system on RN without the Ambrosetti–Rabinowitz condition. Acta Math Sci. 2010;30:1917–1936. doi: 10.1016/S0252-9602(10)60183-X
  • Li GB, Ye H. Existence of positive solutions to semilinear elliptic systems in RN with zero mass. Acta Math Sci. 2013;33(4):913–928. doi: 10.1016/S0252-9602(13)60050-8
  • Miyagaki OH, Souto MAS. Super-linear problems without Ambrosetti and Rabinowitz growth condition. J Differ Equ. 2008;245:3628–3638. doi: 10.1016/j.jde.2008.02.035
  • Pucci P, Rădulescu V. Remarks on a polyharmonic eigenvalue problem. Comptes Rendus Math. 2010;348(3–4):161–164. doi: 10.1016/j.crma.2010.01.013
  • Sirakov B. Standing wave solutions of the nonlinear Schrödinger equation in RN. Ann Mat. 2002;181:73–83. doi: 10.1007/s102310200029
  • Lions PL. The concentration-compcatness principle in the calculus of variations, the locally compact case I. Ann De L'Institut Henri Poincare (C) Non Linear Anal. 1984;1(2):109–145. doi: 10.1016/S0294-1449(16)30428-0
  • Lions PL. The concentration-compcatness principle in the calculus of variations, the locally compact case II. Ann De L'Institut Henri Poincare (C) Non Linear Anal. 1984;1(4):223–282. doi: 10.1016/S0294-1449(16)30422-X
  • Bahri A, Lions PL. On the existence of a positive solution of semilinear elliptic equations in unbounded domains. Ann De L'Institut Henri Poincare (C) Non Linear Anal. 1997;14(3):365–413. doi: 10.1016/S0294-1449(97)80142-4
  • 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. doi: 10.1002/cpa.3160410302
  • Bahrouni A, Repovš DD. Existence and nonexistence of solutions for p(x)- curl systems arising in electromagnetism. Complex Var Elliptic Equ. 2018;63(2):292–301. doi: 10.1080/17476933.2017.1304390
  • Hamdani MK, Harrabi A, Mtiri F, et al. Existence and multiplicity results for a new p(x)−Kirchhoff problem. Nonlinear Anal. 2020;190:111598. doi: 10.1016/j.na.2019.111598
  • Hamdani MK, Repovš DD. Existence and non-existence results for p(x)-curl systems arising in electromagnetism. J Math Anal Appl. 2019; accepted
  • Papageorgiou NS, Rădulescu VD, Repovš DD. Nonlinear analysis- theory and methods. Cham: Springer; 2019. Springer Monographs in Mathematics.
  • Rădulescu VD, Repovš DD. Partial differential equations with variable exponents. Boca Raton, FL: CRC Press; 2015. Variational methods and qualitative analysis. Monographs and Research Notes in Mathematics
  • Kryszewski W, Szulkin A. Generalized linking theorem with an application to semilinear Schrödinger. Adv Differ Equ. 1998;3:441–472.
  • Benci V, Rabinowitz PH. Critical point theorems for indefinite functionals. Invent Math. 1979;52:241–273. doi: 10.1007/BF01389883
  • Li GB, Szulkin A. An asymptically periodic Schrödinger equation with indefinite linear part. Commun Contemp Math. 2002;4:763–776. doi: 10.1142/S0219199702000853
  • He H. Nonlinear Schrödinger equations with sign-changing potential. Adv Nonlinear Stud. 2012;12:237–253. doi: 10.1515/ans-2012-0204
  • Harrabi A. On the Palais–Smale condition. J Funct Anal. 2014;267:2995–3015. doi: 10.1016/j.jfa.2014.07.001
  • Hamdani MK. On a nonlocal asymmetric Kirchhoff problems. Asian-Eur J Math. 2019. doi: 10.1142/S1793557120300018
  • Hamdani MK. Multiple solutions for semi-linear Δλ-Laplace equation without odd nonlinearity. Asian-European J. Math.. 2019. doi:10.1142/S1793557120501314
  • Hamdani MK, Harrabi A. High-order Kirchhoff problems in bounded and unbounded domains, (arXiv:1807.11040v3 [math.AP]); 2019.

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.