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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<ξ,η<1,0<a<1/(1-ξ),0<b<1/η and aξ(1-b)+(1-a)(1-bη)=0, using the coincidence degree theory, the authors establish lower and upper solutions for the following BVP

x '' (t)=f(t,x(t)),t(0,1),x(0)=ax(ξ),x(1)=bx(η)·

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.

34B10Nonlocal and multipoint boundary value problems for ODE