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Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations. (English) Zbl 1133.34011

The following higher-order three-point boundary value problem is considered \[ u^{(n)}+f(t,u,u',\dots,u^{(n-1)})=0 , \qquad t \in (0,1)\,, \]
\[ u(0)= u'(0)= \dots=u^{(n-2)}(0)=u^{(n-2)}(1)- \xi u^{(n-2)}(\eta)=0 \,, \] where \(\,0< \eta < 1,\,\xi>0 \,\) are two constants satisfying \( 0<\xi\eta<1\,. \) The authors give conditions on \(f\) and two pairs of lower and upper solutions (method of Henderson and Thompson) and use topological degree theory to ensure the existence of at least three solutions of the problem. An example is considered to illustrate how to verify the assumptions that guarantee the existence of solutions.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47H11 Degree theory for nonlinear operators
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