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Existence of at least three solutions of a second-order three-point boundary value problem. (English) Zbl 1101.34005

Summary: We study the existence of at least three solutions in the presence of two lower and two upper solutions of some second-order nonlinear three-point boundary value problem of the type
\[ -x''=f(t,x,x'),\quad t\in I=[0,1], \]
\[ x(0)=0,\quad x(1)=\delta x(\eta),\quad 0<\delta\eta<1,\quad 0<\eta<1. \]
The growth of \(f\) with respect to \(x'\) is allowed to be quadratic. We use some degree theory arguments to get the multiplicity result.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47H11 Degree theory for nonlinear operators
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