54
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Semilinear Robin problems driven by the Laplacian plus an indefinite potential

ORCID Icon
Pages 573-587 | Received 12 Dec 2018, Accepted 15 Mar 2019, Published online: 03 Apr 2019

References

  • Shi S, Li S. Existence of solutions for a class of semilinear elliptic equations with the Robin boundary value condition. Nonlinear Anal. 2009;71:3292–3298. doi: 10.1016/j.na.2009.01.209
  • Qian A, Li C. Infinitely many solutions for a Robin boundary value problem. Int J Differ Equ. 2010;2010(548702):1–9.
  • Zhang J, Li S, Xue X. Multiple solutions for a class of semilinear elliptic problems with Robin boundary condition. J Math Anal Appl. 2012;388:435–442. doi: 10.1016/j.jmaa.2011.09.066
  • Papageorgiou NS, Rădulescu VD. Robin problems with indefinite, unbounded potential and reaction of arbitrary growth. Rev Mat Complut. 2016;29:91–126. doi: 10.1007/s13163-015-0181-y
  • D'Aguì G, Marano SA, Papageorgiou NS. Multiple solutions to a Robin problem with indefinite weight and asymmetric reaction. J Math Anal Appl. 2016;433:1821–1845. doi: 10.1016/j.jmaa.2015.08.065
  • Papageorgiou NS, Papalini F. Seven solutions with sign information for sublinear equations with indefinite and unbounded potential and no symmetries. Israel J Math. 2014;201:761–796. doi: 10.1007/s11856-014-1050-y
  • Kyritsi S, Papageorgiou NS. Multiple solutions for superlinear Dirichlet problems with an indefinite potential. Ann Mat Pura Appl. 2013;192:297–315. doi: 10.1007/s10231-011-0224-z
  • Gasiński L, Papageorgiou NS. Multiplicity of solutions for Neumann problems with an indefinite and unbounded potential. Commun Pure Appl Anal. 2013;12:1985–1999. doi: 10.3934/cpaa.2013.12.1985
  • Papageorgiou NS, Rădulescu VD. Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity. Contemp Math. 2013;595:293–315. doi: 10.1090/conm/595/11801
  • Papageorgiou NS, Rădulescu VD, Repovš DD. Double-phase problems with reaction of arbitrary growth. Z Angew Math Phys. 2018;69(108):1–21.
  • Papageorgiou NS, Vetro C, Vetro F. On a Robin (p,q)-equation with a logistic reaction. Opuscula Math. 2019;39:227–245. doi: 10.7494/OpMath.2019.39.2.227
  • Amann H. Saddle points and multiple solutions of differential equations. Math Z. 1979;169:127–166. doi: 10.1007/BF01215273
  • Castro A, Lazer AC. Critical point theory and the number of solutions of a nonlinear Dirichlet problem. Ann Mat Pura Appl. 1979;120:113–137. doi: 10.1007/BF02411940
  • Papageorgiou NS, Rădulescu VD, Repovš DD. Resonant semilinear Robin problems with a general potential. Electron J Qual Theory Differ Equ. 2017;2017(70):1–15. doi: 10.14232/ejqtde.2017.1.70
  • Papageorgiou NS, Vetro C, Vetro F. Pairs of solutions for Robin problems with an indefinite and unbounded potential, resonant at zero and infinity. Manuscripta Math. 2019;158:487–503. doi: 10.1007/s00229-018-1044-x
  • Wang X-J. Neumann problems of semilinear elliptic equations involving critical Sobolev exponents. J Differ Equ. 1991;93:283–310. doi: 10.1016/0022-0396(91)90014-Z
  • Motreanu D, Motreanu VV, Papageorgiou NS. Topological and variational methods with applications to nonlinear boundary value problems. New York: Springer; 2014.
  • Gasiński L, Papageorgiou NS. Nonlinear analysis. Boca Raton: Chapman and Hall/CRC Press; 2006. (Ser. Math. Anal. Appl.; 9).
  • Tang C-L, Wu X-P. Periodic solutions for second order systems with not uniformly coercive potential. J Math Anal Appl. 2001;259:386–397. doi: 10.1006/jmaa.2000.7401
  • Brezis H, Nirenberg L. Remarks on finding critcal points. Commun Pure Appl Anal. 1991;44:939–963. doi: 10.1002/cpa.3160440808
  • Papageorgiou NS, Rădulescu VD. Multiple solutions with precise sign for nonlinear parametric Robin problems. J Differ Equ. 2014;256:2449–2479. doi: 10.1016/j.jde.2014.01.010

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.