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Existence and iteration of monotone positive solutions for multipoint boundary value problem with $$p$$-Laplacian operator. (English) Zbl 1095.34009
The authors give a way to find the solution of a multipoint boundary value problem with $$p$$-Laplacian operator. The main tool is the classical monotone iterative technique establish by H. Amann. The paper closes with the example
$\left(| u'|^3 u'\right)' (t)+\frac{1}{t(1-t)} \left[(u(t))^m+\ln\left((u(t))^k+1\right)\right]=0, \quad t\in(0,1),$
$u'(0) = \sum_{i=1}^n\alpha_i u'(\xi_i), \quad u(1) = \sum_{i=1}^n\beta_i u(\xi_i),$
where $$0\leq k$$, $$m<4$$, $$\xi_i\in(0,1)$$ and $$\alpha_i, \beta_i\in (0,1)$$ such that $$0\leq \sum_{i=1}^n\alpha_i, \sum_{i=1}^n \beta_i <1$$. Monotone technique for $$p$$-Laplacian was used also in other papers like [R. P. Agarwal, Haishen Lu and D. O’Regan, Mem. Differ. Equ. Math. Phys. 28, 13–31 (2003; Zbl 1052.34020)].

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations
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##### References:
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