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VALUE FUNCTIONS AND ERROR BOUNDS OF TRUST REGION METHODS
Zhao, Wenling,Wang, Changyu 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
This paper studies some properties of the value functions and gives some sufficient and necessary conditions about the presented global error and local error. And it leads to one kind of relationship between iterative points and optimal solution or K-T point.
Positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian operator
Fuyi Xu,Zhaowei Meng,Wenling Zhao 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
In this paper, we study the existence of positive solutions for the following nonlinear m-point boundary value problem with p-Laplacian: We show that there exists one or two positive solutions by using fixed-point theorem for operator on a cone. The conclusions in this paper essentially extend and improve the known results.
POSITIVE SOLUTIONS FOR MULTIPOINT BOUNDARY VALUE PROBLEMS WITH ONE-DIMENSIONAL p-LAPLACIAN OPERATOR
Xu, Fuyi,Meng, Zhaowei,Zhao, Wenling Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
In this paper, we study the existence of positive solutions for the following nonlinear m-point boundary value problem with p-Laplacian: $\{{{{(\phi_p(u'))'\;+\;f(t,u(t))=0, \;0<t<1,} \atop u'(0)={\sum}{^{m-2}_{i=1}}\;a_iu'(\xi_i),} \atop u(1)={\sum}{^k_{i=1}}\;b_iu(\xi_i)\;-\;{\sum}{^s_{i=k+1}}\;b_iu(\xi_i)\;-\;{\sum}{^{m-2}_{i=s+1}}\;b_iu'(xi_i),}$ where ${\phi}_p(s)$ is p-Laplacian operator, i.e., ${\phi}_p(s)=\mid s\mid^{p-2}s$, p>1, ${\phi}_q\;=\;({\phi}_p)^{-1}$, $\frac{1}{p}+\frac{1}{q}=1$, $1\;{\leq}\;k\;{\leq}\;s\;{\leq}m\;-\;2$, $b_i\;{\in}\;(0,+{\infty})$ with $0\;<\;{\sum}{^k_{k=1}}\;b_i\;-\;{\sum}{^s_{i=k+1}}\;b_i\;<\;1$, $0\;<\;{\sum}{^{m-2}_{i=1}}\la_i\;<\;1$, $0\;<\;{\xi}_1\;<\;{\xi}_2\;<\;{\cdots}\;<\;{\xi}_{m-2}\;<\;1$, $f\;{\in}\;C([0,\;1]\;{\times}\;[0,\;+{\infty}),\;[0,\;+{\infty}))$. We show that there exists one or two positive solutions by using fixed-point theorem for operator on a cone. The conclusions in this paper essentially extend and improve the known results.