Riv. Mat. Univ. Parma, Vol. 14, No. 1, 2023

Mustapha Ait Hammou [a]

\(p(x)\)-biharmonic problem with Navier boundary conditions

Pages: 33-44
Received: 2 October 2021
Accepted in revised form: 1 June 2022
Mathematics Subject Classification: 35G30, 46E35, 47H11.
Keywords: Navier boundary conditions, variable exponent spaces, Topological degree.
Authors address:
[a]: Laboratory LAMA, Department of Mathematics, Faculty of sciences Dhar el Mahraz, Sidi Mohammed ben Abdellah university, Fez, Morocco.

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Abstract: In this article, we study the following \(p(x)\)-biharmonic problem with Navier boundary conditions \[ \left\{\begin{array}{llcc} -\Delta_{p(x)}^2u=\lambda |u|^{p(x)-2}u+f(x,u), &x\in\Omega,&\\[6px] u=\Delta u=0, &x\in\partial\Omega,& \end{array}\right. \] where \(f\) is a Carathéodory function satisfying only a growth condition. Using the Berkovits degree theory, we establish the existence of at least one weak solution of this problem.

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