Singularly perturbed phenomena of semilinear second order systems (Q810723)

The authors consider the boundary value problem \(\epsilon x''=F(t,x,\epsilon)\), \(a<t<b\), \(x(a,\epsilon)=A(\epsilon)\), \(x(b,\epsilon)=B(\epsilon)\). x, F, A, and B are N-dimensional Euclidean vectors. The authors examine the above general vector system and show that the scalar theory can be used to establish the existence and asymptotic behavior of the solution. Some definitions regarding stability are given in the paper.