Riv. Mat. Univ. Parma, Vol. 14, No. 1, 2023
Mustapha Ait Hammou ^{[a]}
\(p(x)\)biharmonic problem with Navier boundary conditions
Pages: 3344
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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