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Quasilinearization and Multiple Solutions of the Second Order Nonlinear Boundary Value Problem

Journal Name:

  • Journal of Control Engineering and Technology

Publication Year:

  • 2014

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Abstract (Original Language): 
We consider a two-point nonlinear boundary value problem for the second order differential equation. The conditions are provided for existence of multiple solutions. First we show that a quasi-linear problem has a solution of definite type which corresponds to the type of the principal linear part. Multiple solutions are obtained by repeatedly reducing the original equation to quasi-linear ones and proving the appropriate estimates for solutions of modified problems.
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REFERENCES

References: 

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I. Yermachenko and F. Sadyrbaev, “Quasilinearization and multiple solutions of the Emden-Fowler type equation”, Math. Modelling and Analysis, 2005, vol.1, pp. 41–50.
F. Sadyrbaev and I. Yermachenko, “Multiple solutions of two-point nonlinear boundary value problems”, Elsevier Ltd., Nonlinear Analysis, 2009, e176 - e185.
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S. Bernfeld and V. Lakshmikantham, An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York, 1974.

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