Accesso libero

Existence and multiplicity results for a Steklov problem involving (p(x), q(x))-Laplacian operator

INFORMAZIONI SU QUESTO ARTICOLO

Cita

[1] E. Acerbi and G. Mingione, Regularity results for a class of functionals with nonstandard growth, Arch. Ration. Mech. Anal. 156 (2001), no. 2, 121–140.10.1007/s002050100117 Search in Google Scholar

[2] G. A. Afrouzi, Three solutions for a Dirichlet boundary value problem involving the p-Laplacian. Nonlinear Anal. 66(2007), 2281-2288.10.1016/j.na.2006.03.019 Search in Google Scholar

[3] S. N.Antontsev and J. F. Rodrigues, On stationary thermorheological viscous flows, Ann. Univ. Ferrara Sez. VII Sci. Mat. 52 (2006) 19–36.10.1007/s11565-006-0002-9 Search in Google Scholar

[4] M. Bocea and M. Mihăilescu: Γ-convergence of power-law functionals with variable exponents, Nonlinear Analysis 73 (2010), 110-121.10.1016/j.na.2010.03.004 Search in Google Scholar

[5] M. Bocea, M. Mihăilescu, and C. Popovici: On the asymptotic behavior of variable exponent power-law functionals and applications, Ricerche di Matematica 59 (2010), 207-238.10.1007/s11587-010-0081-x Search in Google Scholar

[6] M. Bocea, M. Mihăilescu, M. Pérez-Llanos, and J. D. Rossi: Models for growth of heterogeneous sandpiles via Mosco convergence, Asymptotic Analysis 78 (2012), 11-36.10.3233/ASY-2011-1083 Search in Google Scholar

[7] G. Bonanno, P. Candito, Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian. Arch. Math. (Basel), 80(2003), 424-429.10.1007/s00013-003-0479-8 Search in Google Scholar

[8] G. Bonanno, R. Livrea, Multiplicity theorems for the Dirichlet problem involving the p-Laplacian. Nonlinear Anal. 54(2003), 1-7.10.1016/S0362-546X(03)00027-0 Search in Google Scholar

[9] G. Bonanno, G. Molica Bisci, V. Rădulescu, Multiple solutions of generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems. Nonlinear Anal. Real World Appl. 12(2011), 2656-2665.10.1016/j.nonrwa.2011.03.012 Search in Google Scholar

[10] M. M. Boureanu, D. N. Udrea, Existence and multiplicity results for elliptic problems with p(.)-Growth conditions. Nonlinear Anal. Real World Appl. 14(2013), 1829-1844.10.1016/j.nonrwa.2012.12.001 Search in Google Scholar

[11] Y. Chen, S. Levine and R. Ran, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), 1383–1406.10.1137/050624522 Search in Google Scholar

[12] 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

[13] L. Diening, P. Harjulehto, P. Hästö, M. Ružička, Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Mathematics, vol. 2017, Springer-Verlag, Berlin, 2011.10.1007/978-3-642-18363-8 Search in Google Scholar

[14] X. L. Fan, X. Y. Han, Existence and multiplicity of solutions for p(x)-Laplacian equations inN. Nonlinear Anal. 59(2004), 173-188.10.1016/S0362-546X(04)00254-8 Search in Google Scholar

[15] 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)00150-5 Search in Google Scholar

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

[17] G. Fragnelli, Positive periodic solutions for a system of anisotropic parabolic equations, J. Math. Anal. Appl. 73 (2010), 110–121. Search in Google Scholar

[18] O. Kovácik, J. Rákosnik, On spaces Lp(x) and Wk,p(x). Czechoslovak Math. J. 41(1991), 592-618.10.21136/CMJ.1991.102493 Search in Google Scholar

[19] Q. Liu, Existence of three solutions for p(x)-Laplacian equations. Nonlinear Anal. 68(2008), 2119-2127.10.1016/j.na.2007.01.035 Search in Google Scholar

[20] M. Mihăilescu, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator. Nonlinear Anal. 67(2007), 1419-1425.10.1016/j.na.2006.07.027 Search in Google Scholar

[21] W. Orlicz, Über konjugierte Exponentenfolgen, Studia Math., 3 (1931), 200–21110.4064/sm-3-1-200-211 Search in Google Scholar

[22] K.R. Rajagopal and M. Ružička: Mathematical modeling of electrorheological materials, Contin. Mech. Thermodyn. 13 (2001), 59-78.10.1007/s001610100034 Search in Google Scholar

[23] B. Ricceri, Existence of three solutions fo a class of elliptic eigenvalue problems. Math. Comput. Modelling. 32(2000), 1485-1494.10.1016/S0895-7177(00)00220-X Search in Google Scholar

[24] 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

[25] M. Ružička: Flow of shear dependent electrorheological fuids: unsteady space periodic case, Applied Nonlinear Analysis, 485-504, Kluwer/Plenum, New York, 1999.10.1007/0-306-47096-9_33 Search in Google Scholar

[26] M. Ružička:Electrorheological fuids: modeling and mathematical theory, Lecture Notes in Mathematics 1748, Springer-Verlag, Berlin, 2000. Search in Google Scholar

[27] K. Saoudi, Existence and multiplicity of solutions for a quasilinear equation involving the p(x)-Laplace operator, Complex Variables and Elliptic Equations, 62 (3), 318-332 (2017).10.1080/17476933.2016.1219999 Search in Google Scholar

[28] K Saoudi, A Ghanmi, A multiplicity results for a singular equation involving the p(x)-Laplace operator, Complex Variables and Elliptic Equations 62 (5), 695-725 (2017).10.1080/17476933.2016.1238466 Search in Google Scholar

[29] K. Saoudi, M. Kratou, and S. Alsadhan, Multiplicity results for the Laplacian equation with singular nonlinearities and nonlinear Neumann Boundary Condition, Int. J. Differ. Equ. 2016 (Article ID 3149482), 15 (2016).10.1155/2016/3149482 Search in Google Scholar

[30] X. Shi, X. Ding, Existence and multiplicity of solutions for a general p(x)-Laplacian Neumann problem. Nonlinear Anal. 70(2009), 3715-3720.10.1016/j.na.2008.07.027 Search in Google Scholar

[31] J. Simon, Régularité de la solution d’une équation non linéaire dansN. Vol.665 of Lecture Notes in Math., Springer, Berlin, (1978), 205-227.10.1007/BFb0061807 Search in Google Scholar

[32] A. Zerouali, B. Karim, O. Chakrone, A. Anane, Existence and Multiplicity results for elliptic problems with Nonlinear Boundary conditions and variable exponents. Bol. Soc Paran. Mat. (3s)v. 33 2 (2015), 123-133.10.5269/bspm.v33i2.23355 Search in Google Scholar

[33] V. V. Zhikov: Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk SSSR Ser. Mat., 50 (1986), 675–710. Search in Google Scholar

eISSN:
2351-8227
Lingua:
Inglese