Journal of Mathematical Sciences

, Volume 205, Issue 6, pp 832–847 | Cite as

Quasilinearization of Resonant Boundary-value Problems with Mixed Boundary Conditions

  • N. SveikateEmail author
  • F. SadyrbaevEmail author

We consider resonant problems of the form (i) x″ + p(t)x′ + q(t)x = f(t, x, x′), (ii) x′(0) = 0, x(T) = 0, where p, q, and f are continuous functions, and a homogeneous problem (iii) x″ + p(t)x′ + q(t)x = 0 with the boundary conditions (ii), which has a nontrivial solution. The problem is studied by modifying the linear part and applying the procedure of quasilinearization to the modified problem.


Cauchy Problem Linear Part Trivial Solution Multiple Solution Homogeneous Problem 
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  1. 1.
    R. P. Agarwal and D. O’Regan, Ordinary and Partial Differential Equations, Springer, New York (2009).zbMATHGoogle Scholar
  2. 2.
    R. Conti, “Equazioni differenziali ordinarie quasilineari con condizioni lineari,” Ann. Mat. Pura Appl., 57, 49–67 (1962).CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    M. Dobkevich, “On nonmonotone approximation schemes for solutions of the second-order differential equations,” Different. Integr. Equat., 26, No. 9–10, 1169–1178 (2013).zbMATHMathSciNetGoogle Scholar
  4. 4.
    L. É. lsgol’ts, Differential Equations and Variational Calculus [in Russian], Nauka, Moscow (1969).Google Scholar
  5. 5.
    F. G. Tricomi, Differential equations, Blackie, London (1961).zbMATHGoogle Scholar
  6. 6.
    I. Yermachenko and F. Sadyrbaev, “Types of solutions and multiplicity results for two-point nonlinear boundary value problems,” Nonlin. Anal., 63, e1725–e1735 (2005).CrossRefzbMATHGoogle Scholar
  7. 7.
    I. Yermachenko and F. Sadyrbaev, “Quasilinearization and multiple solutions of the Emden–Fowler-type equation,” Math. Model. Anal., 10, No. 1, 41–50 (2005).zbMATHMathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Daugavpils UniversityDaugavpilsLatvia
  2. 2.University of LatviaRigaLatvia

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