Traveling wave solutions of a gradient system: solutions with a prescribed winding number. II
Author:
David Terman
Journal:
Trans. Amer. Math. Soc. 308 (1988), 391-412
MSC:
Primary 35K57; Secondary 20E05, 35B99
DOI:
https://doi.org/10.1090/S0002-9947-1988-0946449-9
Part I:
Trans. Amer. Math. Soc. (1) (1988), 369-389
MathSciNet review:
946449
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Abstract: This paper completes the analysis begun in [2] concerning the existence of traveling wave solutions of a system of the form ,
. In [2] a notion of winding number for solutions was defined, and the proof that there exists a traveling wave solution with a prescribed winding number was reduced to a purely algebraic problem. In this paper the algebraic problem is solved.
- [1] D. Terman, Infinitely many traveling wave solutions of a gradient system, Trans. Amer. Math. Soc. (to appear). MR 882703 (88i:35082)
- [2] -, Traveling wave solutions of a gradient system: Solutions with a prescribed winding number. I, Trans. Amer. Math. Soc. 308 (1988), 369-389. MR 946449 (89h:35162)
- [3] -, Infinitely many radial solutions of an elliptic system, Ann. Inst. H. Poincaré, Analyse Non Linéaire 4 (1987), 549-604. MR 929475 (89k:35084)
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DOI:
https://doi.org/10.1090/S0002-9947-1988-0946449-9
Article copyright:
© Copyright 1988
American Mathematical Society