61
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Existence and multiplicity of solutions for resonant-superlinear problems

ORCID Icon, ORCID Icon & ORCID Icon
Pages 857-871 | Received 10 Oct 2022, Accepted 26 Dec 2022, Published online: 16 Jan 2023

References

  • Cuesta M, Figueiredo D, Srikanth P. On a resonant-superlinear elliptic problem. Calc Var Partial Differ Equ. 2003;17(3):221–233.
  • Cuesta M, De Coster C. A resonant-superlinear elliptic problem revisited. Adv Nonlinear Stud. 2013;13(1):97–114.
  • De Coster C. Sign-changing solutions and multiplicity results for elliptic problems via lower and upper solutions. NoDEA Nonlinear Differ Equ Appl. 2009;16(6):745–769.
  • Brezis H, Turner REL. On a class of superlinear elliptic problems. Commun Partial Differ Equ. 1977;2(6):601–614.
  • da Silva ED, Ribeiro B. Resonant-superlinear elliptic problems using variational methods. Adv Nonlinear Stud. 2015;15(1):157–169.
  • Papageorgiou NS, Winkert P. Asymmetric (p, 2)-equations, superlinear at +∞, resonant at −∞. Bull Sci Math. 2017;141(5):443–488.
  • Clément P, Peletier LA. An anti-maximum principle for second-order elliptic operators. J Differ Equ. 1979;34(2):218–229.
  • Papageorgiou NS, Zhang C. Nonlinear singular problems with indefinite potential and a superlinear perturbation. Complex Var Elliptic Equ. 2021;66(11):1881–1903.
  • Papageorgiou NS, Zhang C. Singular (p, q)-equations with competing perturbations. Appl Anal. 2022;101(17):6151–6171.
  • Papageorgiou NS, Zhang C. Multiple ground state solutions with sign information for double phase robin problems. Israel J Math. 2022. DOI:10.1007/s11856-022-2370-y
  • Bai YR, Papageorgiou NS, Zeng SD. A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian. Math Z. 2022;300(1):325–345.
  • Zeng SD, Bai YR, Gasinski L, et al. Existence results for double phase implicit obstacle problems involving multivalued operators. Calc Var Partial Differ Equ. 2020;59(1):1–18.
  • Zeng SD, Rădulescu VD, Winkert P. Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions. SIAM J Math Anal. 2022;54(2):1898–1926.
  • Zeng SD, Migorski S, Liu ZH. Nonstationary incompressible Navier-Stokes system governed by a quasilinear reaction-diffusion equation (in Chinese). Sci Sin Math. 2022;52(3):331–354.
  • Gasiński L, Papageorgiou NS. Nonsmooth critical point theory and nonlinear boundary value problems. Boca Raton (FL): Chapman and Hall/CRC Press; 2005.
  • Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1983.
  • Papageorgiou NS, Rădulescu VD, Repovš DD. Nonlinear analysis – theory and methods. Cham: Springer; 2019. (Springer monographs in mathematics).
  • Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 1998.
  • Ambrosetti A, Arcoya D. An introduction to nonlinear functional analysis and elliptic problems. Boston (MA): Birkhäuser; 2011. (PNLDE; vol. 82).
  • 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 (FL): Chapman and Hall/CRC Press; 2006. (Ser math anal appl; vol. 9).
  • Gasiński L, Papageorgiou NS. Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential. Set-Valued Var Anal. 2012;20(3):417–443.
  • Caffarelli LA, Friedman A. Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. J Differ Equ. 1985;60(3):420–433.
  • Lou H. On singular sets of local solutions for p-Laplace equations. Chinese Ann Math Ser B. 2008;29(5):521–530.

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.