Ramzi Alsaedi, Vicentiu D. Radulescu
Abstract:
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 email: ramzialsaedi@yahoo.co.uk |
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Vicentiu D. Radulescu Faculty of Applied Mathematics AGH University of Science and Technology al. Mickiewicza 30, 30-059 Krakow, Poland email: radulescu@inf.ucv.ro |
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