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Resonant Problems by Quasilinearization

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  • Nadezhda Sveikate

Abstract

The Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain and if solutions of the quasilinear problem are in , then the original problem has a solution. We say then that the original problem allows for quasilinearization. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples.

Suggested Citation

  • Nadezhda Sveikate, 2014. "Resonant Problems by Quasilinearization," International Journal of Differential Equations, Hindawi, vol. 2014, pages 1-8, April.
    • Handle: RePEc:hin:jnijde:564914
    DOI: 10.1155/2014/564914
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