Abstract
We consider the Gellerstedt problem for an equation of mixed type with the Lavrent’ev-Bitsadze operator in the leading part and with advanced-retarded multiple deviations of the argument in the derivatives and the function. We prove the uniqueness theorem for the problem without restrictions on the deviation value. The problem is uniquely solvable. We derive closed-form integral representations of the solutions.
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Zarubin, A.N., A Boundary Value Problem for an Equation of Mixed Type with a Differential-Difference Operator, Differ. Uravn., 2011, vol. 47, no. 10, pp. 1439–1445.
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Original Russian Text © A.N. Zarubin, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 10, pp. 1308–1315.
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Zarubin, A.N. Gellerstedt problem for a differential-difference equation of mixed type with advanced-retarded multiple deviations of the argument. Diff Equat 49, 1274–1281 (2013). https://doi.org/10.1134/S001226611310008X
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DOI: https://doi.org/10.1134/S001226611310008X