publication . Article . 2012

Existence and iteration of monotone positive solutions for third-order nonlocal BVPs involving integral conditions

Hai-E Zhang; Jian-Ping Sun;
Open Access English
  • Published: 01 Feb 2012 Journal: Electronic Journal of Qualitative Theory of Differential Equations (issn: 1417-3875, eissn: 1417-3875, Copyright policy)
  • Publisher: University of Szeged
Abstract
This paper is concerned with the existence of monotone positive solution for the following third-order nonlocal boundary value problem $u^{\prime \prime \prime }\left(t\right) +f\left( t,u\left( t\right), u^{\prime}\left( t\right)\right) =0,\, 0<t<1$; $u\left( 0\right) =0,$ $au^{\prime}\left( 0\right)-b u^{\prime\prime}\left( 0\right)=\alpha[u],$ $c u^{\prime}\left( 1\right)+d u^{\prime\prime}\left( 1\right)=\beta[u],$ where $f\in C([0,1]\times R^{+}\times R^{+}, R^{+})$, $\alpha[u]=\int_{_{0}}^{1}u(t)dA(t)$ and $\beta[u]=\int_{_{0}}^{1}u(t)dB(t)$ are linear functionals on $C[0,1]$ given by Riemann-Stieltjes integrals. By applying monotone iterative techniques, ...
Subjects
free text keywords: monotone iterative method, positive solutions, nonlocal, integral conditions, Mathematics, QA1-939, Mathematical optimization, Third order, Boundary value problem, Mathematical analysis, Discrete mathematics, Monotone polygon
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publication . Article . 2012

Existence and iteration of monotone positive solutions for third-order nonlocal BVPs involving integral conditions

Hai-E Zhang; Jian-Ping Sun;