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.


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
Full Text: DOI


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