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On solvability of the BVPS for the fourth‐order Emden‐Fowler type equations

Abstract

Solvability of the boundary value problems (BVPs) for the fourth‐order Emden‐Fowler type equations x (4) = q(t)|x| p sgn x is investigated by using the quasilinearization process. We modify the equation to a quasi‐linear form x( 4) – k 4 x = Fk (t,x) for various values of k. Our considerations are based on a fact that the modified quasi‐linear problem has a solution of the same oscillatory type as the linear part x (4) – k 4 x has. We show that original problem in some cases also has a solution of definite type and establish sufficient conditions for multiple solutions of the given BVP.


First Published Online: 14 Oct 2010

Keyword : quasi‐linear equation, quasilinearization, i‐nonresonant linear part, i‐type solution

How to Cite
Yermachenko, I. (2007). On solvability of the BVPS for the fourth‐order Emden‐Fowler type equations. Mathematical Modelling and Analysis, 12(2), 267-276. https://doi.org/10.3846/1392-6292.2007.12.267-276
Published in Issue
Jun 30, 2007
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