EXISTENCE OF SOLUTIONS FOR GRADIENT TYPE ELLIPTIC SYSTEMS WITH LINKING METHODS

We study the existence of nontrivial solutions of the Gradient type Dirichlet boundary value problem for elliptic systems of the form $-{\Delta}U(x)={\nabla}F(x,U(x)),x{\in}{\Omega}$, where ${\Omega}{\subset}R^N(N{\geq}1)$ is a bounded regular domain and U = (u, v) : ${\Omega}{\rightarrow}R^2$. To study the system we use the liking theorem on product space.