Abstract
We consider Nekrasov’s integral equation describing water waves of permanent form. Nekrasov’s integral equation is parameterized by a parameterμ. We show the global uniqueness of a positive solution for some range ofμ by numerical verification. We also prove them analytically when the solution is very close to the bifurcation point. We thus give a partial answer to a problem which has been open for more than forty years.
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Kobayashi, K. Numerical verification of the global uniqueness of a positive solution for Nekrasov’s equation. Japan J. Indust. Appl. Math. 21, 181 (2004). https://doi.org/10.1007/BF03167471
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DOI: https://doi.org/10.1007/BF03167471