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On a Class of Integral InequalitiesJournal of The London Mathematical Society-second Series
- Publisher
- de Gruyter
- Copyright
- © 1999 Plenum Publishing Corporation
- ISSN
- 1072-947X
- eISSN
- 1072-9176
- DOI
- 10.1515/GMJ.1999.537
- Publisher site
- See Article on Publisher Site
Abstract
In the rectangle 𝐷 = (0, 𝑎) × (0, 𝑏) with the boundary क the Dirichlet problem 𝑢(𝑥, 𝑦) = 0 for (𝑥, 𝑦) ∈ क is considered, where 𝑝 and 𝑞 : 𝐷 → ℝ are locally summable functions and may have nonintegrable singularities on क. 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.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 1999
Keywords: Fourth order linear singular hyperbolic equation; Dirichlet problem; existence; uniqueness and stability of a solution