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Quasilinearization and multiple solutions of the Emden‐Fowler type equation

    I. Yermachenko Affiliation
    ; F. Sadyrbaev Affiliation

Abstract


Existence and multiplicity of solutions of the problem x” = ‐q(t|x|p sign x (i), x(0) = x(1) = 0 (ii) are investigated by reducing equation (i) to a quasi‐linear one so that both equations are equivalent in some domain O. If a solution of corresponding quasi‐linear problem is located in the domain of equivalence O, then this solution solves the original problem also. If this process of quasilinearization is possible for multiple essentially different linear parts, then multiple solutions to the problem (i), (ii) exist.



Darbe nagrinejamas taip vadinamas Emdeno‐Faulerio kvazitiesines diferencialines lygties homogeninio kraštinio uždavinio sprendiniu egzistavimas ir daugialypumas. Parodyta, kad šio uždavinio sprendinio daugialypumas priklauso nuo tam tikru būdu gautos kvazilinearizuotos lygties tiesines dalies savybiu.


First Published Online: 14 Oct 2010

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

How to Cite
Yermachenko, I., & Sadyrbaev, F. (2005). Quasilinearization and multiple solutions of the Emden‐Fowler type equation. Mathematical Modelling and Analysis, 10(1), 41-50. https://doi.org/10.3846/13926292.2005.9637269
Published in Issue
Mar 31, 2005
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