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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 [{\it 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.

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ODE
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##### References:
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