The continuous dependence of periodic solutions for the periodic quasilinear ordinary differential system containing a parameter
Let A(t,x,\(\lambda\)) be a real \(n\times n\) matrix continuous on \({\mathbb{R}}\times {\mathbb{R}}^ n\times [-\lambda_ 0,\lambda_ 0]\) with T- periodicity in t, F(t,x,\(\lambda\)) an \({\mathbb{R}}^ n\)-valued function continuous on \({\mathbb{R}}\times {\mathbb{R}}^ n\times [-\lambda_ 0,\lambda_ 0]\) with T-periodicity in t, where \(\lambda_ 0>0\) and f(t) an \({\mathbb{R}}^ n\)-valued function continuous on \({\mathbb{R}}\) and T-periodic in t. The authors present results for the dependence on \(\lambda\) of T- periodic solutions for the T-periodic quasilinear ordinary differential system \(x'=A(t,x,\lambda)x+\lambda F(t,x,\lambda)+f(t)\) assuming that there exists a unique T-periodic solution of the associated linear system \(x'=B(t)x+f(t),\) where B(t) is a real \(n\times n\) matrix continuous on \({\mathbb{R}}\) and T-periodic.
quasilinear ordinary differential system
scientific article; zbMATH DE number 4214413
scientific article