Electron. J. Diff. Equ., Vol. 2015 (2015), No. 317, pp. 1-14.

Existence of infinitely many solutions for quasilinear problems with a p(x)-biharmonic operator

Ghasem A. Afrouzi, Saeid Shokooh

Abstract:
By using critical point theory, we establish the existence of infinitely many weak solutions for a class of Navier boundary-value problem depending on two parameters and involving the p(x)-biharmonic operator. Under an appropriate oscillatory behaviour of the nonlinearity and suitable assumptions on the variable exponent, we obtain a sequence of pairwise distinct solutions.

Submitted June 16, 2015. Published December 28, 2015.
Math Subject Classifications: 35D05, 34B18, 35J60.
Key Words: Ricceri's variational principle; infinitely many solutions; Navier condition; p(x)-biharmonic operator.

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Ghasem A. Afrouzi
Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email: afrouzi@umz.ac.ir
Saeid Shokooh
Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran
email: saeid.shokooh@stu.umz.ac.ir

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