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Existence of solutions for two classes of nonlinear third-order three-point boundary values. (Chinese. English summary) Zbl 1340.34071

Summary: We investigate the existence of solutions for nonlinear third-order differential equations \[ x'''=f(t, x, x', x''), t\in [0,1] \] subject to the following two sets of three-point boundary problem conditions: \[ x(0)=0, ax'(0)-bx''(0)=0, x'(1)=\alpha x'(\xi) \] and \[ x'(0)=\beta x'(\eta), x(1)=0, cx'(1)+dx''(1)=0. \] By using the Leray-Schauder degree theory, the existence of solutions for the above boundary value problems are given.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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