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Extremal properties of solutions of special classes of a hyperbolic-type equation. (English. Russian original) Zbl 1262.35148
Math. Notes 92, No. 4, 490-496 (2012); translation from Mat. Zametki 92, No. 4, 533-540 (2012).
Summary: Special classes of solutions of the Cauchy problem for a hyperbolic equation are introduced and local extremum principles for the cases of positive and negative values of the parameter of the equation are established.

MSC:
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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[1] V. M. Dolgopolov, M. V. Dolgopolov, and I. N. Rodionova, ”Construction of special classes of solutions for some differential equations of hyperbolic type,” Dokl. Ross. Akad. Nauk 429(5), 583–589 (2009) [Dokl. Math. 80(3), 860–866 (2009)]. · Zbl 1180.35330
[2] H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1: The Hypergeometric Function, Legendre Functions (McGraw-Hill, New York-Toronto-London, 1953; Nauka, Moscow, 1965 and 1973 (2nd ed.)).
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