In weighted C-spaces, we establish the solvability of a boundary-value problem for a semilinear elliptic equation of order 2m in a bounded domain with generalized functions given on its boundary, strong power singularities at some points of the boundary, and finite orders of singularities on the entire boundary. The behavior of the solution near the boundary of the domain is analyzed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 4, pp. 472–493, April, 2009.
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Lopushans’ka, H.P. Generalized boundary values of the solutions of semilinear elliptic equations from weighted functional spaces. Ukr Math J 61, 566–591 (2009). https://doi.org/10.1007/s11253-009-0234-9
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DOI: https://doi.org/10.1007/s11253-009-0234-9