On solvability of the BVPS for the fourth‐order Emden‐Fowler type equations
DOI: https://doi.org/10.3846/1392-6292.2007.12.267-276Abstract
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
Keywords:
quasi‐linear equation, quasilinearization, i‐nonresonant linear part, i‐type solutionHow to Cite
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Copyright (c) 2007 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2007 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.