We explore the sign properties of eigenvalues and the basis properties of eigenvectors for a special quadratic matrix polynomial and use the results obtained to solve the corresponding linear system of differential equations on the half line subject to an initial condition at $t=0$ and a condition at $t=\infty$.
ATALAN, FERİHE and GUSEINOV, GUSEIN SH.
"Solving an initial boundary value problem on thesemiinfinite interval,"
Turkish Journal of Mathematics: Vol. 40:
2, Article 8.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/8