Eigenvalues of the boundary-value problem for a system of second-order linear differential equations with a small parameter of fractional rank in the derivative (Q1057413)

The authors consider the system \(\epsilon^{p/q}x''(t)+A(t,\epsilon)x=0\) with boundary conditions \(x(0,\epsilon)=x(L,\epsilon)=0\) where \(A(t,\epsilon)=\sum_{s\geq 0}\epsilon^ sA_ s(t)\). They give conditions on eigenvalues of \(A_ 0\) to obtain an expansion for the fundamental matrix for small \(\epsilon\), a necessary and sufficient condition guaranteeing the existence of a nontrivial solution, and they get eigenvalues of the above problem.