TY - JOUR
T1 - Perturbations of nonlinear systems of differential equations, III
AU - Brauer, Fred
AU - Strauss, Aaron
N1 - Funding Information:
* Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No. DA-31-124-ARO-D-462. + The research of the first author was supported by the U. S. Army Research Office, Contract No. DA-31-124-ARO-D-268. + The second author was supported in part by NSF grant GP-8914.
PY - 1970/7
Y1 - 1970/7
N2 - Several perturbation theorems are proved for nonlinear ordinary differential systems x′ = f(t, x) for which the zero solution is uniformly stable in variation. This type of stability is, in general, more restrictive than uniform stability but is equivalent to it in the linear case. Under various growth conditions on g(t, x), the behavior of solutions of x′ = f(t, x) + g(t, x) is studied.
AB - Several perturbation theorems are proved for nonlinear ordinary differential systems x′ = f(t, x) for which the zero solution is uniformly stable in variation. This type of stability is, in general, more restrictive than uniform stability but is equivalent to it in the linear case. Under various growth conditions on g(t, x), the behavior of solutions of x′ = f(t, x) + g(t, x) is studied.
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U2 - 10.1016/0022-247X(70)90118-6
DO - 10.1016/0022-247X(70)90118-6
M3 - Article
AN - SCOPUS:0040862628
SN - 0022-247X
VL - 31
SP - 37
EP - 48
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -