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

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.

Abstract licence: CC BY

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