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Infinitely many solutions for a class of hemivariational inequalities involving p(x)-Laplacian


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[1] M. Alimohammady, F. Fattahi, Existence of solutions to hemivaritional inequalities involving the p(x)-biharmonic operator, Electron. J. Diff. Equ., 2015(2015), no. 79, 1-12.Search in Google Scholar

[2] M. Allaoui, Existence of solutions for a Robin problem involving the p(x)-Laplacian, Applied Mathematics E-Notes, 14(2014), 107-115.Search in Google Scholar

[3] A. Ambrosetti, A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge Studies in Advanced Mathematics 104. Cambridge: Cambridge University Press, 2007.10.1017/CBO9780511618260Search in Google Scholar

[4] G. Bonannoa, D. Motreanu, P. Winkert, Variational-hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions, J. Math. Anal. Appl. 381(2011), 627-637.10.1016/j.jmaa.2011.03.015Search in Google Scholar

[5] G. Bonannoa, P. Winkert, Multiplicity results to a class of variationalhemivariational inequalities, Topological methods in nonlinear analysis, 43(2)(2014), 493-516.10.12775/TMNA.2014.029Search in Google Scholar

[6] F. H. Clarke, Optimization and nonsmooth analysis, John Wiley & Sons, New York, 1983.Search in Google Scholar

[7] G. D'AGUÌ, Second-order boundary-value problems with variable exponents, Electronic Journal of differential Equations, 2014(2014), no. 68, 1-10.Search in Google Scholar

[8] S. G. Dend, Eigenvalues of the p(x)-laplacian Steklov problem, J. Math. Anal. Appl., 339 (2008), 925-937.10.1016/j.jmaa.2007.07.028Search in Google Scholar

[9] L. Diening, Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(x)() and W1;p(x)(), Math. Nachr. 268(2004), 31-43.10.1002/mana.200310157Search in Google Scholar

[10] D. E. Edmunds, J. Rákosník, Density of smooth functions in Wk;p(x)(); Proc. R. Soc. A, 437(1992), 229-236.Search in Google Scholar

[11] X. L. Fan, D. Zhao, On the generalized Orlicz - Sobolev space Wm;p(x)(); J. Gansu Educ. College, 12(1998), 1-6.Search in Google Scholar

[12] S. Heidarkhani, G. Afrouzi, A. Hadjian, J. henderson, Existence of infinitely many anti-periodic solutions for second-order impulsive differential inclusions, Electronic Journal of differential Equations, 2013(2013), no. 97, 1-13.Search in Google Scholar

[13] A. Kristály, Infinitely many radial non-radial solutions for a class of hemivariational inequalities, Rocky Mountain Journal of Mathematics, Vol. 35, 4(2005), 1173-1190.10.1216/rmjm/1181069682Open DOISearch in Google Scholar

[14] R. Kajikiya, A critical-point theorem related to the symmetric mountain-pass lemma and its applications to elliptic equations, J. Funct. Analysis, 225(2005), 352-370.10.1016/j.jfa.2005.04.005Search in Google Scholar

[15] L. Li, C. Tang, Existence and multiplicity of solutions for a class of p(x)-biharmonic equations, Acta Mathematica Scientia, 33B(1)(2013), 155-170.10.1016/S0252-9602(12)60202-1Search in Google Scholar

[16] G. Sun, K. Teng, Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem, Math. Commun. 183 19(2014), 183-194.Search in Google Scholar

[17] M. C. Wei, C. L. Tang, Existence and Multiplicity of Solutions for p(x)-Kirchhoff-Type Problem in RN, Bull. Malays. Math. Sci. Soc. (2) 36(3)(2013), 767-781.Search in Google Scholar

[18] Y. Ye, C.L. Tang, Multiplicity of solutions for elliptic boundary value problems, Electronic Journal of differential Equations, 2014(2014), No. 140, 1-13.Search in Google Scholar

[19] X. L. Fan, Regularity of minimizers of variational integrals with p(x)-growth conditions, Ann. Math. Sinica, 17A(5)(1996), 557-564.Search in Google Scholar

[20] O. Kováčik , J. Rákosnínk , On spaces Lp(x) and W1;p(x); Czechoslovak Math. J., 41(1991), 592-618.10.21136/CMJ.1991.102493Search in Google Scholar

[21] X. L. Fan, Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problems , Nonlinear Anal., 52(2003), 1843-1852.10.1016/S0362-546X(02)00150-5Search in Google Scholar

[22] L. Li, L. Ding, W. W. Pan, Existence of multiple solutions for a p(x)-biharmonic equation, Electron J Differ Equ, 2013(2013), No. 139, 1-10.Search in Google Scholar

[23] D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous neumann boundary condition, Le Matematiche, Vol. (2010) Fasc. II, 109-119 doi: 10.4418/2010.65.2.12Search in Google Scholar

[24] V. Rădulescu, Nonlinear elliptic equations with variable exponent: old and new, Nonlinear Analysis, Theory, Methods and Applications, 121(2015), 336-369.Search in Google Scholar

[25] V. Rădulescu, D. Repovs, Partial differential equations with variable exponents, Variational Methods and Qualitative Analysis, CRC Press, Taylor & Francis Group, Boca Raton, 2015.10.1201/b18601Search in Google Scholar

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Mathematics, General Mathematics