Advanced search
Publication Cover
Numerical Functional Analysis and Optimization Volume 37, 2016 - Issue 9
Submit an article Journal homepage
194
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Electrorheological Fluids Equations Involving Variable Exponent with Dependence on the Gradient via Mountain Pass Techniques

R. Ayazoglu (Mashiyev)Faculty of Education, Bayburt University, Bayburt, TurkeyCorrespondence[email protected] [email protected]
&
Ismail EkinciogluFaculty of Science and Arts, Dumlupinar University, Kütahya, Turkey
Pages 1144-1157 | Received 10 Sep 2014, Accepted 20 Jun 2016, Published online: 01 Jul 2016

References

  • A. Ambrosetti and P. H. Rabinowitz (1973). Dual variational methods in critical point theory. J. Funct. Anal. 14:349–381.
  • H. Brezis and E. H. Lieb (1983). A relation between pointwise convergence of functions and convergence functionals. Proc. Am. Math. Soc. 8:486–490.
  • M. M. Boureanu, P. Pucci, and V. D. Radulescu (2011). Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent. Complex Var. Elliptic Eqn. 56:755–767.
  • H. Brezis and L. Nirenberg (1991). Remarks on finding critical points. Comm. Pure Appl. Math. 44:939–964.
  • N. T. Chung (2013). Multiple solutions for a class of p(x)-Kirchhoff type problems with Neumann boundary conditions. Adv. Pure Appl. Math. 4(2):165–177.
  • L. Diening, P. Harjuletho, P. Hästö, M. Růžička (2011). Lebesgue and Sobolev Spaces with Variable Exponents. Berlin: Springer-Verlag.
  • X. L. Fan and Q. H. Zhang (2003). Existence of solutions for p(x)-Laplacian Dirichlet problems. Nonlinear Anal. 52:1843–1852.
  • X. L. Fan and D. Zhao (2001). On the spaces Lp(x)(Ω) and Wm, p(x)(Ω). J. Math. Anal. Appl. 263:424–446.
  • X. L. Fan and D. Zhao (1999). A class of De Giorgi type and H ölder continuity. Nonlinear Anal. 36:295–318.
  • X. L. Fan (2007). Global C1, α regularity for variable exponent elliptic equations in divergence form. J. Diff. Eqn. 235:397–417.
  • D. G. de Figueiredo, M. Girardi, and M. Matzeu (2004). Semilinear elliptic equations with dependence on the gradient via Mountain Pass techniques. Diff. Integ. Eqn. 17:119–126.
  • G. M. Figueiredo (2008). Quasilinear equations with dependence on the gradient via Mountain Pass techniques in ℝN. Appl. Math. Comp. 203:14–18.
  • J. V. A. Gonçalves and C. O. Alves (1998). Existence of positive solutions for m-Laplacian equations in ℝN involving critical Sobolev exponents. Nonlinear Anal. 32(1):53–70.
  • L. Iturriaga and S. Lorca (2007). Existence and multiplicity results of degenerate elliptic equatinos with dependence on the gradient. BVP, Art. ID 47218, doi:10.1155/2007/47218.
  • O. Kovăčik and J. Răkosnik (1991). On spaces Lp(x) and Wk, p(x). Czechoslovak Math. J. 41(116):592–618.
  • D. S. Mitrinoviċ, J. E. Pečariċ, and A. M. Finj (1993). Classical and New Inequalities in Analysis. Dordrecht, Germany: Kluwer Academic Publishers.
  • M. Montenegro and M. Montenegro (2000). Existence and nonexistence of solutions for quasilinear elliptic equations. J. Math. Anal. Appl. 245:303–316.
  • P. Pucci and J. Serrin (1984). Extensions of the mountain pass theorem. J. Funct. Anal. 59:185–210.
  • D. Ruiz and A. Suarez (2007). Existence and uniqueness of positive solution of a logistic equation with nonlinear gradient term. Proc. R. Soc. Edinburgh 137(3):555–566.
  • D. Ruiz (2004). A priori estimates and existence of positive solutions for strongly nonlinear problems. J. Dif. Eqn. 199:96–114.
  • M. Růžička (2000). Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics. Berlin: Springer-Verlag.
  • X. Wang and Y. Ding (1995). Existence of multiple solutions to nonlinear elliptic equations in nondivergece form. J. Math. Anal. Appl. 189:617–630.
  • M. Willem (1996). Minimax Theorems. Basel, Germany: Birkhäuser.
  • J. Yin, J. Li, and Y. Ke (2012). Existence of positive solutions for the p(x)-Laplacian equation. Rocky Mountain J. Math. 42(5):1421–1758.

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.