| I. Yermachenko and F. Sadyrbaev. Types of solutions and multiplicity results for two-point fourth order nonlinear boundary value problems |
| Two-point boundary value problems for the fourth order ordinary nonlinear differential equations with monotone right sides are considered. If the respective nonlinear equation can be reduced to a quasi-linear one with a non-resonant linear part and both equations are equivalent in some domain D, and if solutions of the quasi-linear problem lie in D, then the original problem has a solution. We say then that the original problem allows for quasilinearization. We show that a quasi-linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. |