Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 27-37.

Generalized biharmonic problems with variable exponent and Navier boundary condition

Ramzi Alsaedi, Vicentiu D. Radulescu

We study a class of biharmonic problems with Navier boundary condition and involving a generalized differential operator and competing nonlinearities with variable exponent. The main result of this paper establishes a sufficient condition for the existence of nontrivial weak solutions, in relationship with the values of a positive parameter. The proofs combine variational methods with analytic arguments. The approach developed in this paper allows the treatment of several classes of nonhomogeneous biharmonic problems with variable growth arising in applied sciences, including the capillarity equation and the mean curvature problem.

Published September 15, 2018.
Math Subject Classifications: 35J60, 35J20, 46E35.
Key Words: Generalized biharmonic operator; Navier boundary condition; variable exponent.

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Ramzi Alsaedi
Department of Mathematics, Faculty of Sciences
King Abdulaziz University, P.O. Box 80203
Jeddah 21589, Saudi Arabia
Vicentiu D. Radulescu
Faculty of Applied Mathematics
AGH University of Science and Technology
al. Mickiewicza 30, 30-059 Krakow, Poland

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