Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2026 / Cilt: 3 Sayı: 1

On the existence of solutions for a class of fourth order elliptic equations of Kirchhoff type with variable exponent

Pages
35–45
Publication Date
2019-03-31
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In this paper, we consider a class of fourth order elliptic equations of Kirchhoff type with variable exponent

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Objective & Hypothesis:In this paper, we consider a class of fourth order elliptic equations of Kirchhoff type with variable exponent
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Key Findings & Data:In this paper, we consider a class of fourth order elliptic equations of Kirchhoff type with variable exponent
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Conclusion & Impact:In this paper, we consider a class of fourth order elliptic equations of Kirchhoff type with variable exponent
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fourth order elliptic equations · Kirchhoff type problems · Variable exponents

Abstract

In this paper, we consider a class of fourth order elliptic equations of Kirchhoff type with variable exponent

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Cite This Article

Chung, N. T. (2019). On the existence of solutions for a class of fourth order elliptic equations of Kirchhoff type with variable exponent. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 3 Sayı: 1, 35–45. https://doi.org/10.31197/atnaa.495567

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References (30)

  1. G.A. Afrouzi, M. Mirzapour, N.T. Chung, Existence and multiplicity of solutions for Kirchhoff type problems involving p(x)-biharmonic operators, Z. Anal. Anwend., 33 (2014), 289-303.
  2. K.B. Ali, A. Ghanmi, K. Kefi, Minimax method involving singular p(x)-Kirchhoff equation, J. Math. Physics, 58 (2017): 111505.
  3. H. Ansari, S.M. Vaezpour, Existence and multiplicity of solutions for fourth-order elliptic Kirchhoff equations with potential term, Complex Var. Elliptic Equ., 60 (2015), 668-695.
  4. A. Ayoujil, A.R. El Amrouss, On the spectrum of a fourth order elliptic equation with variable exponent,Nonlinear Anal., 71 (2009), 4916-4926.
  5. J.M. Ball, Initial-boundary value for an extensible beam, J. Math. Anal. Appl., 42 (1973), 61-90.
  6. G. Bonanno, A. Chinni, Existence and multiplicity of weak solutions for elliptic Dirichlet problems withvariable exponent, J. Math. Anal. Appl., 418 (2014), 812-827.
  7. M.M. Boureanu, V. Radulescu, D. Repovs, On a (.)-biharmonic problem with no-flux boundary condition,Comput. & Math. Appl., 72 (2016), 2505-2515.
  8. A. Cabada, G.M. Figueiredo, A generalization of an extensible beam equation with critical growth in RN,Nonlinear Anal. Real World Appl., 20 (2014), 134-142.
  9. N.T Chung, Q.A. Ngo, Multiple solutions for a class of quasilinear elliptic equations of p(x)-Laplacian typewith nonlinear boundary conditions, Proc. Royal Soc. Edinburgh Sect. A: Mathematics, 140(2) (2010),259-272.
  10. N.T. Chung, Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities, Complex Var. Elliptic Equ., 58(12) (2013), 1637-1646.
  11. N.T Chung, Existence of solutions for perturbed fourth order elliptic equations with variable exponents,Electron. J. Qual. Theory Differ. Equ., 2018(96) (2018), 1-19.
  12. F. Colasuonno, P. Pucci, Multiplicity of solutions for p(x)-polyharmonic Kirchhoff equations, NonlinearAnal., 74 (2011), 5962-5974.
  13. G. Dai, Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian, Appl.Anal., 92 (2013), 191-210.
  14. L. Ding, L. Li, Two nontrivial solutions for the nonhomogenous fourth order Kirchhoff equation, Z. Anal.Anwend., 36 (2017), 191-207.
  15. L. Diening, P. Harjulehto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents,Lecture Notes, vol. 2017, Springer-Verlag, Berlin, 2011.
  16. D.E. Edmunds, J. Rakosn´ik, Sobolev embedding with variable exponent, Studia Math., 143 (2000), 267-293.
  17. I. Ekeland, On the variational principle, J. Math. Anal. Appl., 47 (1974), 324-353.
  18. M. Ferrara, S. Khademloo, S. Heidarkhani, Multiplicity results for perturbed fourth-order Kirchhoff typeelliptic problems, Appl. Math. Comput., 234 (2014), 316-325.
  19. A. Ghanmi, Nontrivial solutions for Kirchhoff-type problems involving the p(x)-Laplace operator, RockyMountain J. Math., 48(4) (2018), 1145-1158.
  20. K. Kefi, V.D. Radulescu, On a p(x)-biharmonic problem with singular weights, Z. Angew. Math. Phys., 68(2017): 80.
  21. L. Kong, Eigenvalues for a fourth order elliptic problem, Proc. Amer. Math. Soc., 143 (2015), 249-258.
  22. M. Massar, El M. Hssini, N. Tsouli, M. Talbi, Infinitely many solutions for a fourth-order Kirchhoff typeelliptic problem, J. Math. Comput. Sci., 8 (2014), 33-51.
  23. M. Mihailescu, V.D. Radulescu, On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaceswith variable exponent, Proc. Amer. Math. Soc., 135 (2007), 2929-2937.
  24. J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, Vol. 1034, Springer, Berlin,1983.
  25. M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2002.
  26. Y. Song, S. Shi, Multiplicity of solutions for fourth-order elliptic equations of Kirchhoff type with criticalexponent, J. Dyn. Control Syst., 23 (2017), 375-386.
  27. F. Wang, M. Avci, Y. An, Existence of solutions for fourth order elliptic equations of Kirchhoff type, J.Math. Anal. Appl., 409 (2014), 140-146.
  28. F. Wang, Y. An, Existence and multiplicity of solutions for a fourth-order elliptic equation, Bound. ValueProbl., 2012 (2012): 6.
  29. A. Zang, Y. Fu, Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces,Nonlinear Anal., 69 (2008), 3629-3636.
  30. V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR. Izv.,9 (1987), 33-66.