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Existence theorems for a second order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$m$" id="E1"><mml:mi>m</mml:mi></mml:math>-point boundary value problem at resonance

Existence theorems for a second order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$m$" id="E1"><mml:mi>m</mml:mi></mml:math>-point boundary value problem at resonance

Let f : [0, 1] × R 2 → R be function satisfying Caratheodory′s conditions and e ( t ) ∈ L 1 [0, 1]. Let η ∈ (0, 1), ξ i ∈ (0, 1), a i ≥ 0, i = 1, 2, …, m − 2, with , 0 …