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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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