Abstract
We study functions that are harmonic on a strip and satisfy nonlocal boundary conditions, establish constraints that should be imposed on the coefficients in the boundary conditions to guarantee the uniqueness of nonnegative solutions, and present examples when the uniqueness theorems are not true.
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References
V. A. Kondrat'ev and S. D. Éidel'man, “On biharmonic functions that are nonnegative in a semistrip,”Mat. Zametki,15, No. 1, 121–128 (1974).
A. I. Firdman and S. D. Éidel'man, “On the uniqueness of solutions of boundary-value problems for a biharmonic equation,”Ukr. Mat. Zh.,41, No. 4, 581–584 (1990).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 462–467, April, 1994.
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Firdman, A.I., Éidel'man, S.D. On harmonic functions satisfying nonlocal boundary conditions. Ukr Math J 46, 492–498 (1994). https://doi.org/10.1007/BF01060424
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DOI: https://doi.org/10.1007/BF01060424