# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations

### Tom 56 / 1991

Annales Polonici Mathematici 56 (1991), 49-61 DOI: 10.4064/ap-56-1-49-61

#### Streszczenie

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.

• Leszek Gęba