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 \(b\).


34B16 Singular nonlinear boundary value problems for ordinary differential equations
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