We consider a boundary-value problem for a semilinear hyperbolic equation with iterated multidimensional wave operator in the principal part. The theorems on existence, uniqueness, and nonexistence of solutions of this problem are established.
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S. Kharibegashvili and B. Midodashvili, “Solvability of characteristic boundary-value problems for nonlinear equations with iterated wave operator in the principal part,” Electron. J. Different. Equat., No. 72 (2008).
S. Kharibegashvili and B. Midodashvili, “On one boundary value problem for a nonlinear equation with iterated wave operator in the principal part,” Georg. Math. J., 15, No. 3, 541–554 (2008).
S. Kharibegashvili, “Boundary value problems for some classes of nonlinear wave equations,” Mem. Different. Equat. Math. Phys., 46, 1–114 (2009).
O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
A. Kufner and S. Fuˇcik, Nonlinear Differential Equations [Russian translation], Nauka, Moscow (1988).
V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (1993).
E. Mitidieri and S. I. Pokhozhaev, “A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities,” Tr. Mat. Inst. Ros. Akad. Nauk, 234, 3–383 (2001).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 8, pp. 1123–1132, August, 2019.
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Kharibegashvili, S., Midodashvili, B. On the Existence, Uniqueness, and Nonexistence of Solutions of One Boundary-Value Problem for a Semilinear Hyperbolic Equation. Ukr Math J 71, 1282–1293 (2020). https://doi.org/10.1007/s11253-019-01713-9
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DOI: https://doi.org/10.1007/s11253-019-01713-9