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

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Gęba L., Pruszko T.

Annales Polonici Mathematici

1991-1992

tom 56

nr 1

49-61

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Gęba L.

1 Pruszko T.

1 1991

Wyniki wyszukiwania

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