[1] S.Taarabti, Z. El Allali and K. Ben Haddouch, Eigenvalues of the p(x)−biharmonic operator with indefinite weight under Neumann boundary conditions, Bol. Soc. Paran. Mat. (3s.) v. 36 1 (2018): 195-213.
[2] A.R. El Amrouss and Anass ourraoui, Existence of solutions for a boundary problem involving p(x)−biharmonic operator,Bol. soc. Parana. Mat. (3)31 (2013), no. 1,179-192.MR2990539.
[3] K. Ben Haddouch, Z.El Allali, A.Ayoujil and N.Tsouli, Continuous spectrum of a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions, Annals of the University of Craiova, Mathematics and Computer Science Series Volume, 42(1), (2015), Pages 42-55.
[4] K. Ben Haddouch, Z.El Allali, A.Ayoujil, N.Tsouli, S. El Habib and F. Kissi, Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions, Bol. soc. Parana. Mat, v. 34 1 (2016): 253-272.
[5] X. L. Fan, D. Zhao, On the spaces Lp(x)() and Wm,p(x)(), J. Math. Anal. Appl. 263 (2001) 424-446.
[6] M.Milhailescu, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplacian operator, Nonlinear Anal. T.M.A. 67(2007) 1419-1425.
[7] Clarke DC. A variant of the LusternikSchnirelman theory. Indiana University Mathematics Journal22(1972) 6574.
[8] A.R. El Amrouss, F. Moradi, M. Moussaoui, Existence and multiplicity of solutions for a p(x)-Biharmonic problem with Neumann boundary condition, preprint, ref. no. JPAMAA 0101015.
[9] A.R. El Amrouss, F. Moradi, M. Moussaoui, Existence of solutions for fourth-order PDEs with variable exponents, Electron. 153, (2009)1-13.
[10] G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883.
[11] N. T. Chung, Multiplicity results for a class of p(x)-Kirchhoff type equations with combined nonlinearities,Electron. J. Qual. Theory Differ. Equ.,42 (2012), 1-13.
[12] M. Struwe, Variational methods: Applications to Nonlinear Partial Differential Equatios and Hamiltonian systems, Springer-Verlag, Berlin, 1996.
[13] Ghasem A. Afrouzi, Maryam Mirzapour, Problems for p(x)−Kirchhoff type equations.Electronic Journal of differential equations, Vol. 2013 (2013), No. 253, pp. 110.
[14] V.V.Zhikov, Averaging of functionals of the calculus of variations and elasticity theory.Izv. Akad. NaukSSSR Ser. Mat., (1986), 50(4): 675710.
[15] E. Acerbi, G.Mingione, Gradient estimate for the p(x)-Laplacian system, J.Reine Angew. Math, 584 (2005), 117-148.
[16] Chen, S. Levine and M. Rao. Variable exponent, linear growth functionals in image processing, SIAM J. Appl. Math., 66 No. 4, (2006), 1383-1406.
[17] F. Cammaroto and L. Vilasi. Multiple solutions for a Kirchhoff-type problem involving the p(x)-Laplacian operator,Nonlinear Anal.,74 (2011), 1841-1852.
[18] B. Cheng, X.Wu and J. Liu. Multiplicity of nontrivial solutions for Kirchhoff type problems, Boundary Value Problems,Volume 2010, Article ID 268946, 13 pages.
[19] Mustafa Avci, Bilal Cekic and Rabil A.Mashiyev. Existence and multiplicity of the solutions of the p(x)-Kirchoff type equation via genus theory,Math.Meth.Appl.SCI.(2011),34 1751-1759
[20] Aibin Zanga, Yong Fu. Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces,Nonlinear Analysis TMA69 (2008), 3629-3636.
[21] Edmunds, D., R´akosn´ık, J. Sobolev embeddings with variable exponent.stud, Math. 143 (2000) 267-293.
[22] Chang KC. Critical Point Theory and Applications.Shanghai Scientific and Technology Press: Shanghai, (1986).
[23] Krasnoselskii MA. Topological methods in the theory of nonlinear integral equations. MacMillan: New York, 1964.
[24] Francisco Julio S.A. Corrˆeaa and Augusto C´esar dos Reis Costab. On a bi-nonlocal p(x)−Kirchhoff equation via Krasnoselskiis genus. Math. Meth. Appl. Sci. (2014).
[25] Fan XL, Shen JS, Zhao D. Sobolev embedding theorems for spaces Wk,p(x)( ). Journal of Mathematical Analysis and Applications (2001)
[26] L. Diening, Maximal function on Musielak-Orlicz Spacess and generalized Lebesgue spaces, Bull. Sci. Math.129 (2005) 657700.
[27] D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, second ed., in: Grundlehren Math.Wiss., vol. 244, SpringerVerlag, Berlin, 1983.
[28] E.M. Stein. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.
[29] Lars Diening, Petteri Harjulehto Peter Hasto, Michael Ruziscka.Lebesgue and Sobolev Spaces with Variable Exponents .Springer Heidelberg Dordrecht London New York.