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On the solvability of nonlinear partial differential equations of high order with deviating argument in lowest terms

O. I. Bzheumikhova, V. N. Lesev

Kabardino-Balkarian State University, 173 Chernyshevskii str., Nalchik, 360004 Russia

Abstract: We prove the existence of a solution to higher order partial differential equation with discrete deviation of the argument in lowest terms. The proof is carried out by the method of separation of variables. We also investigate the boundary-value problem for a particular case of the corresponding fourth order nonlinear equation.

Keywords: partial differential equation, deviating argument, Fourier method, boundary-value problem, method of asymptotic expansions.

UDC: 517.957

Received: 18.12.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:7, 7–13

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