## A remark on a second-order three-point boundary value problem.(English)Zbl 0801.34025

The author presents some existence results for the BVP, (P) $$x''= f(t,x,x')$$, $$x(0)= 0$$, $$x(\eta)= x(1)$$. The proofs of theorems essentially use an existence result for operator inclusions established by O. N. Ricceri and B. Ricceri [Appl. Anal. 38, 259-270 (1990; Zbl 0706.47038)]. Reading this paper is necessary to understand this work. The presented assertions improve some theorems of C. P. Gupta [J. Math. Anal. Appl. 168, 540-551 (1992; Zbl 0763.34009)].

### MSC:

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

### Citations:

Zbl 0706.47038; Zbl 0763.34009
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