Infinitely many solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces

References

[1] Adams, R. A.: Sobolev Spaces, Academic Press, New York, 1975.Suche in Google Scholar

[2] Bonanno, G.—Molica Bisci, G.: Infinitely many solutions for a Sturm-Liouville boundary value problem, Bound. Value Probl. 2009 (2009), 1–20.10.1155/2009/670675Suche in Google Scholar

[3] Bonanno, G.—D’aguì, G.: On the Neumann problem for elliptic equations involving the p-Laplacian, J. Math. Anal. Appl. 358 (2009), 223–228.10.1016/j.jmaa.2009.04.055Suche in Google Scholar

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

[5] Chen, Y.—Levine, S.—Rao, R.: Functionals with p(x)-growth in image processing, Duquesne University, Department of Mathematics and Computer Science Technical Report 2004-01, available at www.mathcs.duq.edu/~Osel/CLR05SIAPfinal.pdf.Suche in Google Scholar

[6] Clément, PH.—García-Huidobro, M.—Manásevich, R.—Schmitt, K.: Mountain pass type solutions for quasilinear elliptic equations, Calc. Var. Partial Differential Equations 11 (2000), 33–62.10.1007/s005260050002Suche in Google Scholar

[7] Clément, PH.—De Pagter, B.—Sweers, G.—De Thélin, F.: Existence of solutions to a semilinear elliptic system through Orlicz-Sobolev spaces, Mediterr. J. Math. 1 (2004), 241–267.10.1007/s00009-004-0014-6Suche in Google Scholar

[8] Dankert, G.: Sobolev Embedding Theorems in Orlicz Spaces. PhD Thesis, University of Köln, 1966.Suche in Google Scholar

[9] Diening, L.—Harjulehto, P.—Hästö, P.—Ružička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Math. 2017, Springer, Heidelberg, 2011.10.1007/978-3-642-18363-8Suche in Google Scholar

[10] Donaldson, T. K.: Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. Differential Equations 10 (1971), 507–528.10.1016/0022-0396(71)90009-XSuche in Google Scholar

[11] Donaldson, T. K.—Trudinger, N. S.: Orlicz-Sobolev spaces and embedding theorems, J. Funct. Anal. 8 (1971), 52–75.10.1016/0022-1236(71)90018-8Suche in Google Scholar

[12] Fan, X.: Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients, J. Math. Anal. Appl. 312 (2005), 464–477.10.1016/j.jmaa.2005.03.057Suche in Google Scholar

[13] García-Huidobro, M.—Le, V. K.—Manásevich, R.—Schmitt, K.: On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting, Nonlinear Differential Equations Appl. (NoDEA) 6 (1999), 207–225.10.1007/s000300050073Suche in Google Scholar

[14] Gossez, J. P.: A strongly nonlinear elliptic problem in Orlicz-Sobolev spaces. In: Proc. Sympos. Pure Math. 45, American Mathematical Society, Providence, RI, 1986, pp. 455–462.10.1090/pspum/045.1/843579Suche in Google Scholar

[15] Gossez J. P.—Manásevich, R.: On a nonlinear eigenvalue problem in Orlicz-Sobolev spaces, Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), 891–909.10.1017/S030821050000192XSuche in Google Scholar

[16] Halsey, T. C.: Electrorheological fluids, Science 258 (1992), 761–766.10.1126/science.258.5083.761Suche in Google Scholar

[17] Krasnoseľskii M. A.—Rutickii, YA. B.: Convex Functions and Orlicz Spaces, Noordhoff, Gröningen, 1961.Suche in Google Scholar

[18] Luxemburg, W.: Banach Function Spaces. PhD Thesis, Technische Hogeschool te Delft, The Netherlands, 1955.Suche in Google Scholar

[19] Molica Bisci, G.—Rădulescu, V.: Multiple symmetric solutions for a Neumann problem with lack of compactness, C. R. Acad. Sci. Paris, Ser. I 351 (2013), 37–42.10.1016/j.crma.2012.12.001Suche in Google Scholar

[20] Musielak, J.: Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, Berlin, 1983.10.1007/BFb0072210Suche in Google Scholar

[21] Nakano, H.: Modulated Semi-ordered Linear Spaces, Maruzen Co. Ltd. Tokyo, 1950.Suche in Google Scholar

[22] Omari, P.—Zanolin, F.: Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential, Comm. Partial Diff. Equ. 21 (1996), 721–733.10.1080/03605309608821205Suche in Google Scholar

[23] Omari, P.—Zanolin, F.: An elliptic problem with arbitrarily small positive solutions, Electron. J. Differential Equations Conf. 05 (2000), 301–308.Suche in Google Scholar

[24] O’Neill, R.: Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc. 115 (1965), 300–328.10.1090/S0002-9947-1965-0194881-0Suche in Google Scholar

[25] Orlicz, W.: Über konjugierte Exponentenfolgen, Studia Math. 3 (1931), 200–212.10.4064/sm-3-1-200-211Suche in Google Scholar

[26] Pfeiffer, C.—Mavroidis, C.—Bar-Cohen, Y.—Dolgin, B.: Electrorheological fluid based force feedback device. In: Proc. 1999 SPIE Telemanipulator and Telepresence Technologies VI Conf., Boston, vol. 3840, 1999, pp. 88–99.10.1117/12.369269Suche in Google Scholar

[27] Pucci, P.—Rădulescu, V.: Remarks on a polyharmonic eigenvalue problem, C. R. Acad. Sci. Paris, Ser. I. 348 (2010), 161–164.10.1016/j.crma.2010.01.013Suche in Google Scholar

[28] Rao, M. M.—Ren, Z. D.: Theory of Orlicz Spaces, Dekker, New York, 1991.Suche in Google Scholar

[29] Ricceri, B.: A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401–410.10.1016/S0377-0427(99)00269-1Suche in Google Scholar

[30] Ružička, M.: Electrorheological Fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2000.10.1007/BFb0104029Suche in Google Scholar

[31] Zeidler, E.: Nonlinear Functional Analysis and its Applications, vol. III, Springer, Berlin, 1985.10.1007/978-1-4612-5020-3Suche in Google Scholar