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Existence of three solutions for a Navier boundary value problem involving the p(x)-biharmonic

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The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p(x)-biharmonic operators with Navier boundary value conditions. The technical approach is mainly based on a three critical points theorem due to Ricceri [11].

Abstract

The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p(x)-biharmonic operators with Navier boundary value conditions. The technical approach is mainly based on a three critical points theorem due to Ricceri [11].

참고문헌 (15)

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  3. G. Bonanno, "Some remarks on a three critical points theorem", Nonlinear Anal, 54(4), pp.651~665 (2003)
  4. X. L. Fan, "Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients", J. Math. Anal. Appl, 312(2), pp.464~477 (2005)
  5. X. L. Fan, "On the spaces Lp(x) and Wm,p(x)", J. Math. Anal. Appl, 263(2), pp.424~446 (2001)
  6. H. Hudzik, "On generalized Orlicz-Sobolev space", Funct. Approx. Comment. Math, 4, pp.37~51 (1976)
  7. O. Kovacik, "On spaces Lp(x) and Wk,p(x)", Czechoslovak Math. J, 41(4), pp.592~618 (1991)
  8. S. Kichenassamy, "Singular solutions of the p-Laplace equation", Math. Ann, 275(4), pp.599~615 (1986)
  9. C. Li, "Three solutions for a Navier boundary value problem involving the p-biharmonic", Nonlinear Anal, 72(3), pp.1339~1347 (2010)
  10. S. Liu, "On the existence of solutions to a fourth-order quasilinear resonant problem", Abstr. Appl. Anal, 7(3), pp.125~133 (2002)
  11. B. Ricceri, "A three critical points theorem revisited", Nonlinear Anal, 70(9), pp.3084~3089 (2009)
  12. M. Ruzicka, "Electro-rheological Fluids: Modeling and Mathematical Theory", pp.1784~ (2000), Springer-Verlag
  13. S. G. Sanko, "Denseness of C∞ 0 (RN) in the generalized Sobolev spaces Wm,p(x)(RN)", Dokl. Akad. Nauk, 369(4), pp.451~454 (1999)
  14. A. Zang, "Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces", Nonlinear Anal, 69(10), pp.3629~3636 (2008)
  15. B, Nonlinear Mono- tone Operators, "Nonlinear Functional Analysis and its Applications. II", pp.1990, E. Zeidler

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