Multiple solutions of the fourth‐order emden‐fowler equation - Yermachenko, I. (Mathematical Modelling and Analysis, 2006)
Two‐point boundary value problems for the fourth‐order Emden‐Fowler equation are considered. If the given equation can be reduced to a quasi‐linear one with a non‐resonant linear part so that both equations are equivalent in some domain D, and if solution of the quasi‐linear problem is located in D, then the original problem has a solution. 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.First Published Online: 14 Oct 2010