## Three solutions for three-point boundary value problems.(English)Zbl 1076.34011

Summary: We study the existence of at least three solutions for the three-point nonlinear boundary value problems $u''(t)+ a(t) f(u)= 0,\quad 0< t< 1;\qquad u(0)= 0= u(1)-\gamma u(\eta),$ with $$\eta\in (0,1)$$, $$\gamma\in [0,1)$$, $$a\in C([0, 1],(0,\infty))$$ and $$f\in C(\mathbb{R},\mathbb{R})$$. Without any monotonicity assumptions on the nonlinear term $$f$$, by using the increasing operator theory and approximation process, we prove that the three-point boundary value problems has at least three solutions.

### MSC:

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

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