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Dirichlet BVP for the second order nonlinear ordinary differential equations at resonance

    Sulkhan Mukhigulashvili Affiliation
    ; Mariam Manjikashvili Affiliation

Abstract

Landesman-Lazer’s type efficient sufficient conditions are established for the solvability of the Dirichlet problem , for where ;R) and f is the L([a,b]; R) Caratheodory function, in the case where the linear problem has nontrivial solutions. The results obtained in the paper are optimal in the sense that if , i.e., when nonlinear equation turns to the linear equation, from our results follows the first part of Fredholm’s theorem.

Keyword : nonlinear ordinary differential equation, Dirichlet problem at resonance

How to Cite
Mukhigulashvili, S., & Manjikashvili, M. (2019). Dirichlet BVP for the second order nonlinear ordinary differential equations at resonance. Mathematical Modelling and Analysis, 24(4), 585-597. https://doi.org/10.3846/mma.2019.035
Published in Issue
Oct 25, 2019
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