Dirichlet BVP for the second order nonlinear ordinary differential equations at resonance
DOI: https://doi.org/10.3846/mma.2019.035Abstract
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.
Keywords:
nonlinear ordinary differential equation, Dirichlet problem at resonanceHow to Cite
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Copyright (c) 2019 The Author(s). Published by Vilnius Gediminas Technical University.
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