Existence and multiplicity of solutions for a p(x)-biharmonic problem with Neumann boundary conditions
DOI:
https://doi.org/10.5269/bspm.42168Abstract
In this paper, we study the p(x)-biharmonique problem with Neumann boundary conditions. Using the three critical point Theorem, we establish the existence of at least three solutions of this problem.
References
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X. L. Fan, Eigenvalues of the p(x)- Laplacian Neumann problems. Nonlinear Anal. 67 (2007) 2982-2992. https://doi.org/10.1016/j.na.2006.09.052
X. L. Fan, X. Fan, A Knobloch-type result for p(t) Laplacian systems. J. Math. Anal. Appl. 282 (2003) 453-464. https://doi.org/10.1016/S0022-247X(02)00376-1
X. L. Fan, Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003) 1843-1852. https://doi.org/10.1016/S0362-546X(02)00150-5
X. L. Fan, Q. H. Zhang and D. Zhao, Eigenvalues of p(x)- Laplacian Dirichlet problem. J. Math. Anal. Appl. 302 (2005), 306-317. https://doi.org/10.1016/j.jmaa.2003.11.020
X. L. Fan and D. Zhao, On the space Lp(x)(Ω) and Wm,p(x)(Ω), J. Math. Anal. Appl. 263 (2001) 424-446. https://doi.org/10.1006/jmaa.2000.7617
D.Gilbarg & N.S.Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1983.
T. C. Halsey, Electrorheological fluids, Science 258 (1992), 761-766. https://doi.org/10.1126/science.258.5083.761
P. Harjulehto, P. Hasto, Ut Van Le, M. Nuortio, Overview of differential equations with non-standard growt h, preprint (2009).
R. B. Israel & R. A. Adams, Sobolev Space. August 2002.
M. Mihailescu, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear Anal. 67 (2007) 1419-1425. https://doi.org/10.1016/j.na.2006.07.027
B. Ricceri, On three critical points theorem. Arch.Math. (Basel) 75, 220-226 (2000). https://doi.org/10.1007/s000130050496
M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, 2000. https://doi.org/10.1007/BFb0104029
L. L. Wang Y. H. Fan & W. G. Ge, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator. Nonlinear Analysis. (2009), vol. 71, no. 9, pp. 4259-4270. https://doi.org/10.1016/j.na.2009.02.116
J. H. Yao, Solution for Neumann boundary problems involving the p(x)-Laplace operators, Nonlinear Anal. T.M.A. 68 (2008) 1271-1283. https://doi.org/10.1016/j.na.2006.12.020
E.Zeidler, Nonlinear Function Analysis and its Applications, vol.II/B: Nonlinear Monotone Operators, Springer, New York, 1990. https://doi.org/10.1007/978-1-4612-0981-2
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2021-12-16
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