Multiple solutions for a system of equations with \(p\)-Laplacian
The authors study the existence of multiple critical points of strongly indefinite nonsmooth functionals using the Limit Index, defined in \textit{Y. Q. Li} [Nonlinear Anal. TMA 25, No. 12, 1371--1389 (1995; Zbl 0847.58014)]. The results are then applied to the following boundary value problem: \[ \begin{cases} \Delta_p u=F_u(x,u,v) & \text{in }\Omega,\\ -\Delta_p v=F_v(x,u,v) & \text{in }\Omega,\\ u, v=0 & \text{on } \partial \Omega,\end{cases} \] where \(\Delta_p u=\text{div} (| \nabla u| ^{p-2}\nabla u)\), \(\Omega\) is a bounded domain in \({\mathbb R}^N\), and \(u,v\in W^{1,p}_0(\Omega)\), \(1<p<N\). Under appropriate conditions on the function \(F(x,u,v)\), the system possesses an unbounded sequence of weak solutions.
scientific article; zbMATH DE number 5362101