Multiple solutions of the fourth‐order emden‐fowler equation

Abstract

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.

Key words:

• quasi‐linear equation
• quasilinearization
• conjugate point
• i‐nonresonant linear part
• i‐type solution