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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2019 / Cilt: 3 - Sayı: 1

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

Nguyen Thanh CHUNG
Pages
35–45
Publication Date
2019-03-31
DOI
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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:Research Article
📍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://ajindex.com/articles/729158

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References (17)

  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 variat