The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind

Details The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind

2008-04-03

arxiv.org/abs/0804.0542v2

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

We consider a problem of finding vanishing at infinity $C^1([0,\oo))$-solutions to non-homogeneous system of linear ODEs which has the pole of first order at $x=0$. The resonant case where the corresponding homogeneous problem has nontrivial solutions is of main interest. Under the conditions that the homogeneous system is exponentially dichotomic on $[1,\oo)$ and the residue of system's operator at $x=0$ does not have eigenvalues with real part 1, we construct the so called generalized Green function. We also establish conditions under which the main non-homogeneous problem can be reduced to the Noetherian one with nonzero index.

Affiliated with

Also associated with

No associations

Rating

The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The integral representation of solutions to a boundary value problem on the half-line for a system of linear ODEs with singularity of first kind will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-352480