Abstract
We prove theorems giving conditions sufficient for the existence of homoclinic orbits for two dimensional, time-dependent vector fields which are autonomous for all sufficiently large values of the independent variable. We give applications to second order equations such as those arising in waveguide studies as well as explicit examples which illustrate our assumptions.
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Dedicated to Klaus Kirchgässner on the occasion of his sixtieth birthday
Research supported by the National Science Foundation under DMS 87-03656 and the U. S. Army Office through the Mathematical Sciences Institute of Cornell University, Contract DAAG-29-85C-0018.
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Holmes, P.J., Stuart, C.A. Homoclinic orbits for eventually autonomous planar flows. Z. angew. Math. Phys. 43, 598–625 (1992). https://doi.org/10.1007/BF00946253
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DOI: https://doi.org/10.1007/BF00946253