Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations
Volume 56 / 1991
Annales Polonici Mathematici 56 (1991), 49-61
DOI: 10.4064/ap-56-1-49-61
Abstract
This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in $Ω ⊂ ℝ^n$, $u = Du = ... = D^{m-1}u$ on ∂Ω in the Sobolev space $W_0^{m,2}(Ω)$, 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.
