Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 163, pp. 1-9.
Title: Infinitely many solutions for class of
Navier boundary (p,q)-biharmonic systems
Authors: Mohammed Massar (Univ. Mohamed I, Oujda, Morocco)
El Miloud Hssini (Univ. Mohamed I, Oujda, Morocco)
Najib Tsouli (Univ. Mohamed I, Oujda, Morocco)
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.