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On a nonlocal boundary value problem for second-order nonlinear singular differential equations. (English) Zbl 0967.34011

Authors’ summary: Criteria for the existence and uniqueness of a solution to the boundary value problem \[ u''= f(t,u,u'),\quad u(a+)= 0,\quad u(b-)= \int^b_a u(s) d\mu(s), \] are established, where \(f\):\(]a, b[\times \mathbb{R}^2\to \mathbb{R}\) satisfies the local Carath√©odory conditions, and \(\mu: [a,b]\to \mathbb{R}\) is a function of bounded variation. These criteria apply to the case where the function \(f\) has nonintegrable singularities in the first argument at the points \(a\) and \(b\).

MSC:

34B16 Singular nonlinear boundary value problems for ordinary differential equations
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