Matches in SemOpenAlex for { <https://semopenalex.org/work/W2548949507> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2548949507 abstract "In this survey, we recall the formulation of the prob- lems and give a review of some nontrivial results in the area. Let F = (F1, ..., Fn ): R n → R n be a C 1 map and let F � (x )a nd JacF (x )= det F � (x) denote the Jacobian matrix and the jacobian of F at ap ointx ∈ R n , respectively. The Global Asymptotic Stability Problem (GASP) reads as follows: Assume that F (0) = 0 and at any point x ∈ R n all eigenvalues of F � (x) have negative real parts. Then consider the associated system of differential equations x � (t )= Fj (x1(t), ..., xn(t)), j =1 , ..., n. The question is whether the solution x(t) = 0 is globally asymptotically stable. If n> 2, then the answer is negative (even if F is a a polynomial automorphism), so from now on (GASP) denotes (GASP) restricted to R 2 . In 1963, Olech showed that under the (GASP) assumption (i. e., Jac F (x) > 0 and Tr ace F � (x )= ∂F 1 ∂x1 (x )+ ∂F2 ∂x2 (x) < 0 for any x ∈ R 2 ) the conclu-" @default.
- W2548949507 created "2016-11-11" @default.
- W2548949507 creator A5017489783 @default.
- W2548949507 date "2005-01-01" @default.
- W2548949507 modified "2023-09-23" @default.
- W2548949507 title "On the global asymptotic stability problem and the Jacobian conjecture 1" @default.
- W2548949507 cites W150950198 @default.
- W2548949507 cites W162626055 @default.
- W2548949507 cites W1974572477 @default.
- W2548949507 cites W1974950624 @default.
- W2548949507 cites W1990257884 @default.
- W2548949507 cites W2035280681 @default.
- W2548949507 cites W2036490427 @default.
- W2548949507 cites W2043009207 @default.
- W2548949507 cites W2044413922 @default.
- W2548949507 cites W2046712067 @default.
- W2548949507 cites W2081461845 @default.
- W2548949507 cites W2087979527 @default.
- W2548949507 cites W2126507098 @default.
- W2548949507 cites W2591478697 @default.
- W2548949507 cites W2724587836 @default.
- W2548949507 cites W2952812327 @default.
- W2548949507 cites W3186394 @default.
- W2548949507 cites W62336006 @default.
- W2548949507 cites W898743806 @default.
- W2548949507 cites W980323180 @default.
- W2548949507 hasPublicationYear "2005" @default.
- W2548949507 type Work @default.
- W2548949507 sameAs 2548949507 @default.
- W2548949507 citedByCount "0" @default.
- W2548949507 crossrefType "journal-article" @default.
- W2548949507 hasAuthorship W2548949507A5017489783 @default.
- W2548949507 hasConcept C114614502 @default.
- W2548949507 hasConcept C118712358 @default.
- W2548949507 hasConcept C121332964 @default.
- W2548949507 hasConcept C134306372 @default.
- W2548949507 hasConcept C158693339 @default.
- W2548949507 hasConcept C200331156 @default.
- W2548949507 hasConcept C2780990831 @default.
- W2548949507 hasConcept C28826006 @default.
- W2548949507 hasConcept C33923547 @default.
- W2548949507 hasConcept C62520636 @default.
- W2548949507 hasConcept C90119067 @default.
- W2548949507 hasConceptScore W2548949507C114614502 @default.
- W2548949507 hasConceptScore W2548949507C118712358 @default.
- W2548949507 hasConceptScore W2548949507C121332964 @default.
- W2548949507 hasConceptScore W2548949507C134306372 @default.
- W2548949507 hasConceptScore W2548949507C158693339 @default.
- W2548949507 hasConceptScore W2548949507C200331156 @default.
- W2548949507 hasConceptScore W2548949507C2780990831 @default.
- W2548949507 hasConceptScore W2548949507C28826006 @default.
- W2548949507 hasConceptScore W2548949507C33923547 @default.
- W2548949507 hasConceptScore W2548949507C62520636 @default.
- W2548949507 hasConceptScore W2548949507C90119067 @default.
- W2548949507 hasLocation W25489495071 @default.
- W2548949507 hasOpenAccess W2548949507 @default.
- W2548949507 hasPrimaryLocation W25489495071 @default.
- W2548949507 hasRelatedWork W1812532787 @default.
- W2548949507 hasRelatedWork W1979291052 @default.
- W2548949507 hasRelatedWork W2021980071 @default.
- W2548949507 hasRelatedWork W2036864977 @default.
- W2548949507 hasRelatedWork W2041703528 @default.
- W2548949507 hasRelatedWork W2045386568 @default.
- W2548949507 hasRelatedWork W2049783645 @default.
- W2548949507 hasRelatedWork W2117879090 @default.
- W2548949507 hasRelatedWork W2127690708 @default.
- W2548949507 hasRelatedWork W2255817952 @default.
- W2548949507 hasRelatedWork W2395332285 @default.
- W2548949507 hasRelatedWork W2953025349 @default.
- W2548949507 hasRelatedWork W2984039156 @default.
- W2548949507 hasRelatedWork W2990539944 @default.
- W2548949507 hasRelatedWork W3009267245 @default.
- W2548949507 hasRelatedWork W3033833707 @default.
- W2548949507 hasRelatedWork W3103409668 @default.
- W2548949507 hasRelatedWork W3115762320 @default.
- W2548949507 hasRelatedWork W88420397 @default.
- W2548949507 hasRelatedWork W2574512751 @default.
- W2548949507 isParatext "false" @default.
- W2548949507 isRetracted "false" @default.
- W2548949507 magId "2548949507" @default.
- W2548949507 workType "article" @default.