Abstract
We consider the following two-point boundary value problems u ″ x + u π − x + g x , u π − x = h x in 0 , π , u 0 = 0 = u π , and u ″ x + u π − x − g x , u π − x = − h x in 0 , π , u 0 = 0 = u π , by setting h ∈ L 1 0 , π and g : 0 , π × R ⟶ R being a Caratheodory function. When a , b ∈ L 1 0 , π , a x ≤ 3 for x ∈ 0 , π a.e. with strict inequality on a positive measurable subset of 0 , π , and g x , u ≤ a x u + b x for x ∈ 0 , π a.e. as well as sufficiently large u , several existence theorems will be obtained, with or without a sign condition.
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