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On the Steklov problem involving the p(x)-laplacian with indefinite weight

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the p(x)-Laplacian [formula] Our approach is based on min-max method and Ekeland's variational principle.
Rocznik
Strony
779--794
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
autor
  • Jazan Technical College P.O. Box: 241 Jazan 45952, Saudi Arabia University of Tunis El Manar Faculty of Sciences 1060 Tunis, Tunisia
autor
  • University of Jeddah Faculty of Science and Arts Mathematics Department Khulais, Saudi Arabia
  • University of Tunis El Manar Faculty of Sciences 1060 Tunis, Tunisia
autor
  • Northern Border University Community College of Rafha Saudi Arabia
  • University of Tunis El Manar Faculty of Sciences 1060 Tunis, Tunisia
Bibliografia
  • [1] A.G. Afrouzi, A. Hadijan, S. Heidarkhani, Steklov problem involving the p{x)-Laplacian, Electron. J. Differential Equations 134 (2014), 1-11.
  • [2] M. Allaoui, A.R. El Amrouss, A. Ourraoui, Existence and multiplicity of solutions for a Steklov problem involving the p(x)-Laplace operator, Electron. J. Differential Equations 132 (2012), 1-12.
  • [3] S.N. Antontsev, S.I Shmarev, A model porous medium equation with variable exponent of nonlinearity: Existence uniqueness and localization properties of solutions, Nonlinear Anal. Theory Methods Appl. 60 (2005), 515-545.
  • [4] K. Benali, M. Bezzarga, On a nonhomoge.ne.ous quasilinear eigenvalue problem in Sobolev spaces with variable exponent, Potential Theory and Stochastics in Albac, Aurel Cornea Memorial Volume, Conference Proceedings Albac, September 4-8, 2007, Theta 2008, 21-34.
  • [5] F. Cammaroto, A. Chinni, B. Di Bella, Multiple solutions for a Neumann problem involving the p(x)-Laplacian, Nonlinear Anal. 71 (2009), 4486-4492.
  • [6] M. Cencelij, D. Repovs, Z. Virk, Multiple perturbations of a singular eigenvalue problem, Nonlinear Anal. 119 (2015), 37-45.
  • [7] Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image processing, SIAM J. Appl. Math. 66 (2006), 1383-1406.
  • [8] G. D'Agui, A. Sciammetta, Infinitely many solutions to elliptic problems with variable exponent and nonhom.oge.ne.ous Neumann conditions, Nonlinear Anal. 75 (2012), 5612-5619.
  • [9] G. Dai, Infinitely many non-negative solutions for a Dirichlet problem, involving p(x)-Laplacian, Nonlinear Anal. 71 (2009), 5840-5849.
  • [10] S.G. Deng, Eigenvalues of the p(x)-Laplacian Steklov problem, J. Math. Anal. Appl. 339 (2008), 925-937.
  • [11] D. Edmunds, J. Rakosnik, Sobolev embeddings with variable exponent, Studia Math. 143 (2000), 267-293.
  • [12] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353.
  • [13] X.L. Fan, X. Han, Existence and multiplicity of solutions for p(x)-Laplacian equations in RN, Nonlinear Anal. 59 (2004), 173-188.
  • [14] X.L. Fan, J.S. Shen, D. Zhao, Sobolev embedding theorems for spaces Wkt'p{x)(Cl), J. Math. Anal. Appl. 262 (2001), 749-760.
  • [15] X.L. Fan, Q.H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), 1843-1852.
  • [16] X.L. Fan, D. Zhao, On the spaces Lp(x>(0.) and Wm'p(x>(Q), J. Math. Anal. Appl. 263 (2001), 424-446.
  • [17] Y. Fu, Y. Shan, On the removability of isolated singular points for elliptic equations involving variable exponent, Adv. Nonlinear Anal. 5 (2016) 2, 121-132.
  • [18] P. Harjulehto, P. Hastó, V. Latvala, Minimizers of the variable exponent, non-uniformly convex Dirichlet energy, J. Math. Pures Appl. 89 (2008), 174-197.
  • [19] C. Ji, Remarks on the existence of three solutions for the p{x)-Laplacian equations, Nonlinear Anal. 74 (2011), 2908-2915.
  • [20] L. Kong, Multiple solutions for fourth order elliptic problems with p(x)-biharm,onic operators, Opuscula Math. 36 (2016) 2, 253-264.
  • [21] O. Kovacik, J. Rakosnik, On spaces Lp(x) and Wk'p(x>, Czechoslovak Math. J. 41 (1991), 592-618.
  • [22] A. Kristaly, V. Radulescu, Cs. Varga, Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems, Encyclopedia ol Mathematics and its Applications, vol. 136, Cambridge University Press, Cambridge, 2010.
  • [23] R.A. Mashiyev, S. Ogras, Z. Yucedag, M. Avci, Existence and multiplicity of weak solutions for nonuniformly elliptic equations with non standard growth condition, Complex Variables and Elliptic Equations 57 (2012) 5, 579-595.
  • [24] N. Mavinga, M.N. Nkashama, Steklov spectrum and nonresonance for elliptic equations with nonlinear boundary conditions, Electron. J. Differential Equations, 19 (2010), 197-205.
  • [25] M. Mihailescu, V. Radulescu, On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent, Proc. Amer. Math. Soc. 135 (2007), 2929-2937.
  • [26] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math. 65, Amer. Math. Soc, Providence, RI, 1986.
  • [27] V. Radulescu, Nonlinear elliptic equations with variable exponent: old and new, Nonlinear Anal. 121 (2015), 336-369.
  • [28] V. Radulescu, D. Repovs, Partial Differential Equations with Variable Exponents, Variational Methods and Qualitative Analysis, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, FL, 2015.
  • [29] D. Repovs, Stationary waves of Schrodinger-type equations with variable exponent, Anal. Appl. (Singap.) 13 (2015) 6, 645-661.
  • [30] M. Ruźicka, Electro-rheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., vol. 1784, Springer-Verlag, Berlin, 2000.
  • [31] Z. Wei, Z. Chen, Existence results for the p{x)-Laplacian with nonlinear boundary conditions, ISRN Applied Mathematics 2012 (2012), Article ID 727398.
  • [32] Z. Yucedag, Solutions of nonlinear problems involving p(x)-Laplacian operator, Adv. Nonlinear Anal 4 (2015) 4, 285-293.
  • [33] V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR. Izv 29 (1987), 33-66.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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