Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations
This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in , on ∂Ω in the Sobolev space , where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.