Abstract
Boundary value problems of ordinary differential equations on infinite intervals are analyzed in terms of a theory which holds under weaker assumptions than the ordinarily applied theory, which requires the fundamental matrix of the system of differential equations to have certain decay properties near infinity. The analysis for linear problems is here done by determining the fundamental matrix of the system of differential equations asymptotically. For inhomogeneous problems a suitable particular solution having a 'nice' asymptotic behavior is chosen and global existence and uniqueness theorems are thereby established in the linear case. The asymptotic behavior of this solution follows immediately. Nonlinear problems are treated by using perturbation techniques involving linearization near infinity and by applying the methods for the linear case. Some problems from fluid dynamics and thermodynamics are treated to illustrate the power of the discussed methods.