Multiplicity of solutions for Robin problem involving the p(x)-laplacian

[1] M. Allaoui, A. El Amrouss and A. Ourraoui, On a Class of Nonlocal p(x)-Laplacian Neumann Problems, Thai Journal of Mathematics, Volume 15 (2017) Number 1, 91–105. Search in Google Scholar

[2] A. Allaoui, A. El Amrouss, A. Ourraoui, Three Solutions For A Quasi-Linear Elliptic Problem, Applied Mathematics E-Notes, 13 (2013), 51–59. Search in Google Scholar

[3] G. A. Afrouzi, A. Hadjian, S. Heidarkhani, Steklove problems involving the p(x)-Laplacian, Electronic Journal of Differential Equations, Vol. 2014 (2014) No. 134, 1–11. Search in Google Scholar

[4] S. Antontsev, S. Shmarev, Handbook of Differential Equations, Stationary Partial Differ. Equ. 3 (2006). Chap. 110.1016/S1874-5733(06)80005-7 Search in Google Scholar

[5] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal., 70 (2009), 3084–3089.10.1016/j.na.2008.04.010 Search in Google Scholar

[6] G. Bonanno, A. Chinnì, Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent, J. Math. Anal. Appl., 418 (2014), 812–827.10.1016/j.jmaa.2014.04.016 Search in Google Scholar

[7] G. Bonanno, S. A. Marano, On the structure of the critical set of nondifferentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1–10.10.1080/00036810903397438 Search in Google Scholar

[8] G. Bonanno, G. Molica Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl., 2009 (2009), 1–20.10.1155/2009/670675 Search in Google Scholar

[9] M. M. Boureanu, Infinitely many solutions for a class of degenerate anisotropic elliptic problems with variable exponent, Taiwanese Journal of Mathematics, 15 (5), 2291–2310.10.11650/twjm/1500406435 Search in Google Scholar

[10] H. Brezis, L. Nirenberg, Remarks on finding critical points, Commun Pure Appl Math., 44 (1991), 939–963. doi:10.1002/cpa.3160440808.10.1002/cpa.3160440808 Search in Google Scholar

[11] J. Chabrowski, Y. Fu, Existence of solutions for p(x)-Laplacian problems on a bounded domain, J. Math. Anal. Appl., 306 (2005), 604–618.10.1016/j.jmaa.2004.10.028 Search in Google Scholar

[12] Y. Chen, S. Levine, R. Rao, Variable exponent, linear growth functionals in image restoration, SIAMJ. Appl. Math., 66 (2006), 1383–1406.10.1137/050624522 Search in Google Scholar

[13] N. T. Chung, Multiple solutions for a class of p(x)-Kirchho type problems with Neumann boundary conditions, Advances in Pure Appl. Math., 4 (2) (2013), 165–177.10.1515/apam-2012-0034 Search in Google Scholar

[14] S.-G. Deng, A local mountain pass theorem and applications to a double perturbed p(x)-Laplacian equations, Appl. Math. Comput., 211 (2009), 234–241. Search in Google Scholar

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

[16] G. Dai, Infinitely many solutions for a p(x)-Laplacian equation in ℝN, Nonlinear Anal., 71 (2009), 1133–1139.10.1016/j.na.2008.11.037 Search in Google Scholar

[17] S.-G. Deng,Positive solutions for Robin problem involving the p(x)-Laplacian, J. Math. Anal. Appl., 360 (2009), 548–560.10.1016/j.jmaa.2009.06.032 Search in Google Scholar

[18] L. Diening, P. Hästö, A. Nekvinda, Open problems in variable exponent Lebesgue and Sobolev spaces, in: P. Drábek, J. Rákosník (Eds.), Proceedings, Milovy, Czech Republic, 2004, pp. 38–58. Search in Google Scholar

[19] X. Fan, X. Han, Existence and multiplicity of solutions for p(x)-Laplacian equations in ℝ^N, Nonlinear Anal., 59 (2004), 173–188. Search in Google Scholar

[20] M. Ferrara, S. Heidarkhani, Multiple solutions for perturbed p-Laplacian boundary-value problems with impulsive effects, Electronic journal of differential equations, n. 2014 (2014), 1–14, ISSN: 1072–6691. Search in Google Scholar

[21] X. Fan, D. Zhao, On the spaces Lp(x)(Ω) and Wm,p(x)(Ω) J. Math. Anal. Appl., 263 (2001), 424–446.10.1006/jmaa.2000.7617 Search in Google Scholar

[22] X. Fan. Eigenvalues of the p(x)-Laplacian Neumann problems, Nonlinear Anal., 67:2982-2992, 2007. http://dx.doi.org/10.1016/j.na.2006.09.052.10.1016/j.na.2006.09.052 Search in Google Scholar

[23] Y. Fu, X. Zhang, A multiplicity result for p(x)-Laplacian problem in ℝ^N, Nonlinear Anal., 70 (2009), 2261–2269.10.1016/j.na.2008.03.038 Search in Google Scholar

[24] A. Ourraoui, Multiplicity results for Steklov problem with variable exponent, Applied Mathematics and Computation, 277 (2016), 34–43.10.1016/j.amc.2015.12.043 Search in Google Scholar

[25] A. Ourraoui, Some Results For Robin Type Problem Involving p(x)−Laplacian, (preprint). Search in Google Scholar

[26] P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations. In CBMS Regional Conference Series in Mathematics, Vol. 65, American Mathematical Soceity, Providence (1986).10.1090/cbms/065 Search in Google Scholar

[27] M. A. Ragusa, A. Tachikawa, Regularity for minimizers for functionals of double phase with variable exponents, Adv. Nonlinear Anal., 9 (2020), 710–728.10.1515/anona-2020-0022 Search in Google Scholar

[28] M. Růžička, Flow of shear dependent electrorheological fluids, CR Math. Acad. Sci. Paris, 329 (1999), 393–398.10.1016/S0764-4442(00)88612-7 Search in Google Scholar

[29] M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2002. Search in Google Scholar

[30] S. Shokooh, A. Neirameh, Existence results of infinitely many weak solutions for p(x)−Lapalacian-Like operators, U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 4, 2016. Search in Google Scholar

[31] E. Zeidler, Nonlinear Functional Analysis and its Applications, vol. II/B, Berlin, Heidelberg, New York, 1985.10.1007/978-1-4612-5020-3 Search in Google Scholar

[32] Q. H. Zhang, Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems, Nonlinear Anal., 70 (2009), 305–316.10.1016/j.na.2007.12.001 Search in Google Scholar

[33] V. Zhikov, Averaging of functionals in the calculus of variations and elasticity, Math. USSR Izv., 29 (1987), 33–66.10.1070/IM1987v029n01ABEH000958 Search in Google Scholar