Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 10
Submit an article Journal homepage
204
Views
13
CrossRef citations to date
0
Altmetric
Articles

On a class of double-phase problem without Ambrosetti–Rabinowitz-type conditions

Bin Gea School of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China;b College of Automation, Harbin Engineering University, Harbin, People's Republic of ChinaCorrespondence[email protected]
View further author information
,
Li-Yan Wangb College of Automation, Harbin Engineering University, Harbin, People's Republic of ChinaView further author information
&
Jian-Fang Lua School of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of ChinaView further author information
Pages 2147-2162 | Received 23 Feb 2019, Accepted 08 Oct 2019, Published online: 16 Oct 2019

References

  • Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Izv Akad Nauk SSSR Ser Mat. 1986;50:675–710.
  • Zhikov VV. On Lavrentiev's phenomenon. Russian J Math Phys. 1995;3:249–269.
  • Zhikov VV. On some variational problems. Russian J Math Phys. 1997;5:105–116.
  • Zhikov VV, Kozlov SM, Oleinik OA. Homogenization of differential operators and integral functionals. Berlin: Springer-Verlag; 1994.
  • Perera K, Squassina M. Existence results for double-phase problems via Morse theory. Commun Contemp Math. 2018;20:1750023. doi: 10.1142/S0219199717500237
  • Papageorgiou NS, Rdulescu VD, Repovš DD. Double-phase problems with reaction of arbitrary growth. Z Angew Math Phys. 2018;69:108. doi: 10.1007/s00033-018-1001-2
  • Cencelj M, Rdulescu VD, Repovš DD. Double phase problems with variable growth. Nonlinear Anal. 2018;177:270–287. doi: 10.1016/j.na.2018.03.016
  • Liu WL, Dai GW. Existence and multiplicity results for double phase problem. J Differ Equ. 2018;265:4311–4334. doi: 10.1016/j.jde.2018.06.006
  • Liu WL, Dai GW. Three ground state solutions for double phase problem. J Math Phys. 2018;59:121503.
  • Mao AM, Zhang ZT. Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition. Nonlinear Anal. 2009;70:1275–1287. doi: 10.1016/j.na.2008.02.011
  • Colasuonno F, Squassina M. Eigenvalues for double phase variational integrals. Ann Mat Pura Appl. 2016;195:1917–1959. doi: 10.1007/s10231-015-0542-7
  • Musielak J. Orlicz spaces and modular spaces. Berlin: Springer; 1983. (Lecture Notes in Math., Vol. 1034).
  • Benkirane A, Sidi El Vally M. Variational inequalities in Musielak-Orlicz-Sobolev spaces. Bull Belg Math Soc Simon Stevin. 2014;21:787–811.
  • Fan X, Guan CX. Uniform convexity of Musielak-Orlicz-Sobolev spaces and applications. Nonlinear Anal. 2010;73:163–175. doi: 10.1016/j.na.2010.03.010
  • Chang KC. Critical point theory and Applications. Shanghai: Shanghai Scientific and Technology Press; 1996.
  • Lee J, Kim YH. Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators. Bound Value Probl. 2016;2016:1–25. doi: 10.1186/s13661-015-0477-3
  • Lee J, Kim JM, Kim YH. Existence and multiplicity of solutions for Kirchhoff-Schrödinger type equations involving p(x)-Laplacian on the entire space RN. Nonlinear Anal RWA. 2019;45:620–649. doi: 10.1016/j.nonrwa.2018.07.016

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.