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Second-order boundary value problems with integral boundary conditions. (English) Zbl 1169.34310
The author studies the existence of positive solutions of the solutions of the second-order boundary value problem $$ y'' = f(t, y(t)), \quad 0 < t < 1, $$ $$ y(0) - ay'(0) = \int_0^1 \! g_0(s) y(s) \, ds, $$ $$ y(1) - by'(1) = \int_0^1 \! g_1(s) y(s) \, ds, $$ where $f:[0, 1] \times \mathbb{R} \to \mathbb{R}$ and $g_0, g_1 : [0, 1] \to [0, +\infty)$ are continuous and, $a$ and $b$ are nonnegative real numbers. The results are based on the classical cone expansion and contraction technique. The author provides and example at the end of the paper to illustrate his technique.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
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