positive solutions for a system of higher order boundary-value problems involving all derivatives of odd orders

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2012
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Abstract
In this article we study the existence of positive solutions for the system of higher order boundary-value problems involving all derivatives of odd orders $$displaylines{ (-1)^mw^{(2m)} =f(t, w, w',-w''',dots, (-1)^{m-1}w^{(2m-1)}, z, z',-z''',dots, (-1)^{n-1}z^{(2n-1)}), cr (-1)^nz^{(2n)} =g(t, w, w',-w''',dots, (-1)^{m-1}w^{(2m-1)}, z, z',-z''',dots, (-1)^{n-1}z^{(2n-1)}), cr w^{(2i)}(0)=w^{(2i+1)}(1)=0quad (i=0,1,dots, m-1),cr z^{(2j)}(0)=z^{(2j+1)}(1)=0quad (j=0,1,dots, n-1). } $$ Here $f,gin C([0,1]imesmathbb{R}_+^{m+n+2},mathbb{R}_+)$ $(mathbb{R}_+:=[0,+infty))$. Our hypotheses imposed on the nonlinearities $f$ and $g$ are formulated in terms of two linear functions $h_1(x)$ and $h_2(y)$. We use fixed point index theory to establish our main results based on a priori estimates of positive solutions achieved by utilizing nonnegative matrices.
Reference Key
wang2012electronicpositive Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Kun Wang, Zhilin Yang
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Journal icsoft 2006 - 1st international conference on software and data technologies, proceedings
Year 2012
DOI
DOI not found
URL
http://ejde.math.txstate.edu/Volumes/2012/52/abstr.html
Keywords
mathematics

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