Zeros of maps of \(R^ n\) into \(R^ n\) (Q1091766)
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scientific article; zbMATH DE number 4011798
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Zeros of maps of \(R^ n\) into \(R^ n\) |
scientific article; zbMATH DE number 4011798 |
Statements
Zeros of maps of \(R^ n\) into \(R^ n\) (English)
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1987
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For the determination of the zeros of a map f from \(R^ n\) into itself the standard homotopy \(H(t,x)=f(x)+(t-1)f(a)\), \(0\leq t\leq 1\), is considered and results are obtained which guarantee that the trajectory either ends at a zero of f or becomes asymptotic to a hyperplane \(t=t_ 0\). These results are then applied to prove two well-known existence theorems for zeros of functions f which are proper on \(R^ n\).
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continuation methods
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homotopy method
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existence of zeros
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