Solvability of the boundary value problems (BVPs) for the fourth‐order Emden‐Fowler type equations x(4) = q(t)|x|psgn x is investigated by using the quasilinearization process. We modify the equation to a quasi‐linear form x(4) – k4x = 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) – k4x 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.
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
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