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Existence and multiplicity of solutions for four-point boundary value problems at resonance. (English) Zbl 1070.34026
Under the assumptions \(0<\xi,\eta<1,0<a<1/(1-\xi),0<b<1/\eta\) and \(a\xi(1-b)+(1-a)(1-b\eta)=0\), using the coincidence degree theory, the authors establish lower and upper solutions for the following BVP \[ x''(t)=f(t,x(t)),\;t\in (0,1),\;\; x(0)=ax(\xi),\;x(1)=bx(\eta). \] By this way, they obtain some existence and multiplicity results for this problem. The results in this paper generalize those in [R. Ma, Nonlinear Anal., Theory Methods Appl. 53, 777–789 (2003; Zbl 1037.34011)], but the methods used are different from those in above mentioned paper.
Reviewer: Yuji Liu (Yueyang)

MSC:
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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