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Existence results for a fourth-order ordinary differential equation with a four-point boundary condition. (English) Zbl 1141.34305

Summary: The fourth-order differential equation
\[ y^{(4)}(t)-f(t,y(t),y''(t))=0,\quad 0\leq t\leq 1, \]
with the four-point boundary value problem
\[ y(0)=y(1)=0,\quad ay''(\xi_1)-by'''(\xi_1)=0,\quad cy''(\xi_2)+dy'''(\xi_2)=0 \]
is studied in this work, where \(0\leq\xi_1<\xi_2\leq 1\). Some results on the existence of at least one positive solution to the above four-point boundary value problem are obtained by using the Krasnoselskii fixed point theorem.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47H10 Fixed-point theorems
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References:

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