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The existence of positive solutions is established for two-point boundary value problems for second-order differential equations with the nonlinearity dependent on the derivative: {(Lφ)(x)=h(x)f(φ(x),φ′(x)),0≤x≤1,R1(φ)≡α1φ(0)+β1φ′(0)=0,R2(φ)≡α2φ(1)+β2φ′(1)=0, where (Lφ)(x)=−(p(x)φ′(x))′+q(x)φ(x). Conditions are given in terms of the relative behaviors of the quotient f(u,v)|u|+|v| for |u|+|v| near...
The classical Krasnosel’skii fixed point theorem concerning cone compression and expansion of norm type is extended; in it the norm is replaced with some convex functional. As an application, the existence of positive solutions for the singular second-order m-point boundary value problem is considered.
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