Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501660 | Journal of Differential Equations | 2005 | 43 Pages |
Abstract
This paper is motivated by the problem of computing the index of an isolated critical point for a certain class of nonlinear elliptic operators. Such a class includes operators A which are defined byãAu,Ïã=â|α|⩽1â«Î©aα(x,u,D1u)DαÏ(x)dx,u,ÏâWËm1(Ω)and are associated with boundary value problems of the type(*)â|α|⩽1(-1)|α|Dαaα(x,u,D1u)+λb(x,u,D1u)=0,xâΩ,(**)u(x)=0,xââΩ,where ΩâRn,n>2, is open, bounded and has a C2-boundary âΩ. As an application of our new abstract theory, we obtain an index formula for such an operator A acting from the Sobolev space WËm1(Ω) into its dual space [WËm1(Ω)]* for 1
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Athanassios G. Kartsatos, Igor V. Skrypnik, Vladimir N. Shramenko,