On the smoothness of solutions of the third order nonlinear differential equation

Abdumauvlen S Berdyshev, Ahtai B Birgebaev, Alberto Cabada
2017 Boundary Value Problems  
In this work we study the following third order differential equation: where q(x, y) ≥ 1 is a continuous function in all its variables. We will deal with the following questions: (a) The existence of a solution to equation (1) in the space L 2 (R) where L 2 (R) is the space of square summable functions. (b) Additional conditions on the third derivative of this solution to belong to the space L 2 (R).
doi:10.1186/s13661-017-0799-4 fatcat:ijxlczoarnbhtbbs5n7ubnkusi