Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.
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1Faculty of Physics, Chair of Higher Mathematics, I. Javakhishvili Tbilisi State University, 3, Chavchavadze Ave., Tbilisi 380028, Georgia
Citation Information: Georgian Mathematical Journal. Volume 6, Issue 6, Pages 537–552, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.1999.537, February 2010
In the rectangle 𝐷 = (0, 𝑎) × (0, 𝑏) with the boundary Γ the Dirichlet problem
𝑢(𝑥, 𝑦) = 0 for (𝑥, 𝑦) ∈ Γ
is considered, where 𝑝 and 𝑞 : 𝐷 → ℝ are locally summable functions and may have nonintegrable singularities on Γ. The effective conditions guaranteeing the unique solvability of this problem and the stability of its solution with respect to small perturbations of the coefficients of the equation under consideration are established.
Key words and phrases.: Fourth order linear singular hyperbolic equation; Dirichlet problem; existence; uniqueness and stability of a solution
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