Electron. J. Diff. Equ., Vol. 2012 (2012), No. 163, pp. 1-9.

Infinitely many solutions for class of Navier boundary (p,q)-biharmonic systems

Mohammed Massar, El Miloud Hssini, Najib Tsouli

Abstract:
This article shows the existence and multiplicity of weak solutions for the (p,q)-biharmonic type system
$$\displaylines{ \Delta(|\Delta u|^{p-2}\Delta u)=\lambda F_u(x,u,v)\quad\hbox{in }\Omega,\cr \Delta(|\Delta v|^{q-2}\Delta v)=\lambda F_v(x,u,v)\quad\hbox{in }\Omega,\cr u=v=\Delta u=\Delta v=0\quad \hbox{on }\partial\Omega. }$$
Under certain conditions on F, we show the existence of infinitely many weak solutions. Our technical approach is based on Bonanno and Molica Bisci's general critical point theorem.

Submitted June 4, 2012. Published September 21, 2012.
Math Subject Classifications: 35J40, 35J60.
Key Words: Navier value problem; infinitely many solutions; Ricceri's variational principle.

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Mohammed Massar
University Mohamed I, Faculty of Sciences
Department of Mathematics, Oujda, Morocco
email: massarmed@hotmail.com
El Miloud Hssini
University Mohamed I, Faculty of Sciences
Department of Mathematics, Oujda, Morocco
email: hssini1975@yahoo.fr
Najib Tsouli
University Mohamed I, Faculty of Sciences
Department of Mathematics, Oujda, Morocco
email: tsouli@hotmail.com

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