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Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side

Author

Listed:
  • Alexander Domoshnitsky
  • Alexander Lomtatidze
  • Abraham Maghakyan
  • Jiří Šremr

Abstract

Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problem ð ‘¢ ( 1 , 1 ) ( ð ‘¡ , ð ‘¥ ) = â„“ 0 ( ð ‘¢ ) ( ð ‘¡ , ð ‘¥ ) + â„“ 1 ( ð ‘¢ ( 1 , 0 ) ) ( ð ‘¡ , ð ‘¥ ) + â„“ 2 ( ð ‘¢ ( 0 , 1 ) ) ( ð ‘¡ , ð ‘¥ ) + ð ‘ž ( ð ‘¡ , ð ‘¥ ) , ð ‘¢ ( ð ‘¡ , ð ‘ ) = ð ›¼ ( ð ‘¡ ) for ð ‘¡ ∈ [ ð ‘Ž , ð ‘ ] , ð ‘¢ ( ð ‘Ž , ð ‘¥ ) = ð ›½ ( ð ‘¥ ) f o r ð ‘¥ ∈ [ ð ‘ , ð ‘‘ ] given on the rectangle [ ð ‘Ž , ð ‘ ] × [ ð ‘ , ð ‘‘ ] are established, where the linear operators â„“ 0 , â„“ 1 , â„“ 2 map suitable function spaces into the space of essentially bounded functions. General results are applied to the hyperbolic equations with essentially bounded coefficients and argument deviations.

Suggested Citation

  • Alexander Domoshnitsky & Alexander Lomtatidze & Abraham Maghakyan & Jiří Šremr, 2011. "Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-26, August.
    • Handle: RePEc:hin:jnlaaa:242965
    DOI: 10.1155/2011/242965
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