Resonant Problems by Quasilinearization

Abstract EN

The Dirichlet resonant boundary value problems are considered.

If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem has a solution.

We say then that the original problem allows for quasilinearization.

If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.

We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples.