Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 15
119
Views
3
CrossRef citations to date
0
Altmetric
Research Article

Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian

ORCID Icon, ORCID Icon &
Pages 5323-5333 | Received 14 Dec 2020, Accepted 31 Jan 2021, Published online: 22 Feb 2021

References

  • Diening L, Harjulehto P, Hästö P, et al. Lebesgue and Sobolev spaces with variable exponents. Heidelberg: Springer-Verlag; 2011. (Lecture Notes in Mathematics; 2017).
  • Fan XL, Zhao D. On the spaces Lp(x)(Ω) and Wm,p(x)(Ω). J Math Anal. 2011;263:424–446.
  • Kováik O, Rákosník J. On the spaces Lp(x) and W1,p(x). Czechoslovak Math. 1991;41:592–618.
  • Rajagopal K, Ruika M. Mathematical modelling of electrorheological materials. Contin Mech Thermodyn. 2001;13:59–78.
  • Ruika M. Electrorheological fluids modeling and mathematical theory. Berlin: Springer–Verlag; 2000.
  • Acerbi E, Mingione G. Regularity results for stationary electro-rheological fluids. Arch Ration Mech Anal. 2002;164:213–259.
  • Zhikov VV. On some variational problem. Russ J Math Phys. 1997;5:105–116.
  • Bulíek M, Glitzky A, Liero M. Systems describing electrothermal effects with p(x)-Laplacian like structure for discontinuous variable exponents. SIAM J Math Anal. 2016;48:3496–3514.
  • Cimatti G. Remark on the existence and uniqueness for the thermistor problem under mixed boundary conditions. Quart Appl Math. 1989;47:117–121.
  • Glitzky A, Liero M. Analysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices. Berlin: WIAS; 2015. (Tech. Rep. 2143).
  • Marano S, Mosconi SJ. Some recent results on the Dirichlet problem for (p,q)-Laplace equations. Discrete Contin Dyn Syst Ser S. 2018;11:279–291.
  • Sciammetta A, Tornatore E. Two positive solutions for a Dirichlet problem with the (p,q)-Laplacian. Math Nachr Math Nachr. 2020;293:1004–1013.
  • Amrouss AE, Ourraoui A, Allaoui M. On the spectrum of (p(x),q(x))-Laplacian in RN. Appl Math E Notes2016;16:11–20.
  • Mihăilescu M, On a class of nonlinear problems involving a p(x)-Laplace type operator. Czechoslovak Math J. 2008;58(133):155–172.
  • Yucedag Z. Infinitely many nontrivial solutions for nonlinear problems involving the (p1(x),p2(x))-Laplace operator. Acta Univ Apulensis. 2014;40:315–331.
  • Carl S, Le VK, Motreanu D. Nonsmooth variational problems and their inequalities, comparison principles and applications. New York (NY): Springer; 2007.
  • Fan XL, Zhang QH. Existence of solutions for p(x)-Laplacian Dirichlet problem. Nonlinear Anal. 2003;52:1843–1852.
  • Motreanu D, Motreanu VV, Papageorgiou NS. Topological and variational methods with applications to nonlinear boundary value problems. New York (NY): Springer; 2014.
  • Bonanno G, D'Aguì G. Two non-zero solutions for elliptic Dirichlet problems. Z Anal Anwend. 2016;35:449–464.
  • Bonanno G, Chinnì A. Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent. J Math Anal Appl. 2014;418:812–827.

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.