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ArticleOriginal scientific text

Title

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

Authors 1, 1

Affiliations

  1. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Abstract

This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in Ω⊂ℝn, u=Du=...=Dm-1u on ∂Ω in the Sobolev space W0m,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.

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Annales Polonici Mathematici
1991-1992/56/1
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Pages:
49-61
Main language of publication
English
Received
1990-04-02
Accepted
1991-03-02
Published
1991
Exact and natural sciences