| I. Yermachenko and F. Sadyrbaev. On solutions of the fourth-order nonlinear boundary value problems |
| We consider a two-point boundary value problem for the fourth-order non-autonomous Emden-Fowler type equation using the quasilinearization process. We reduce the given nonlinear equation to a some quasi-linear one with a non-resonant linear part so that both equations are equivalent in some bounded domain. We use a fact that modified quasi-linear problem has a solution of definite type, which corresponds to the type of the linear part. If a solution of the quasi-linear problem is located in the domain of equivalence, then the original problem has a solution. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. |