Global Behavior of the Components for the Second Order m-Point Boundary Value Problems
We consider the nonlinear eigenvalue problems u″+rf(u)=0, 0<t<1, u(0)=0, u(1)=∑i=1m−2αiu(ηi), where m≥3, ηi∈(0,1), and αi>0 for i=1,…,m−2, with ∑i=1m−2αi<1; r∈â„Â; f∈C1(â„Â,â„Â). There exist two constants s2<...
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2008-02-01
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Series: | Boundary Value Problems |
Online Access: | http://dx.doi.org/10.1155/2008/254593 |
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doaj-f70173b6ed95492783e82f6572592f3c2020-11-25T00:26:18ZengSpringerOpenBoundary Value Problems1687-27622008-02-01200810.1155/2008/254593Global Behavior of the Components for the Second Order m-Point Boundary Value ProblemsRuyun MaYulian AnWe consider the nonlinear eigenvalue problems u″+rf(u)=0, 0<t<1, u(0)=0, u(1)=∑i=1m−2αiu(ηi), where m≥3, ηi∈(0,1), and αi>0 for i=1,…,m−2, with ∑i=1m−2αi<1; r∈â„Â; f∈C1(â„Â,â„Â). There exist two constants s2<0<s1 such that f(s1)=f(s2)=f(0)=0 and f0:=limu→0(f(u)/u)∈(0,∞), f∞:=lim|u|→∞(f(u)/u)∈(0,∞). Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.http://dx.doi.org/10.1155/2008/254593 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ruyun Ma Yulian An |
spellingShingle |
Ruyun Ma Yulian An Global Behavior of the Components for the Second Order m-Point Boundary Value Problems Boundary Value Problems |
author_facet |
Ruyun Ma Yulian An |
author_sort |
Ruyun Ma |
title |
Global Behavior of the Components for the Second Order m-Point Boundary Value Problems |
title_short |
Global Behavior of the Components for the Second Order m-Point Boundary Value Problems |
title_full |
Global Behavior of the Components for the Second Order m-Point Boundary Value Problems |
title_fullStr |
Global Behavior of the Components for the Second Order m-Point Boundary Value Problems |
title_full_unstemmed |
Global Behavior of the Components for the Second Order m-Point Boundary Value Problems |
title_sort |
global behavior of the components for the second order m-point boundary value problems |
publisher |
SpringerOpen |
series |
Boundary Value Problems |
issn |
1687-2762 |
publishDate |
2008-02-01 |
description |
We consider the nonlinear eigenvalue problems u″+rf(u)=0, 0<t<1, u(0)=0, u(1)=∑i=1m−2αiu(ηi), where m≥3, ηi∈(0,1), and αi>0 for i=1,…,m−2, with ∑i=1m−2αi<1; r∈â„Â; f∈C1(â„Â,â„Â). There exist two constants s2<0<s1 such that f(s1)=f(s2)=f(0)=0 and f0:=limu→0(f(u)/u)∈(0,∞), f∞:=lim|u|→∞(f(u)/u)∈(0,∞). Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems. |
url |
http://dx.doi.org/10.1155/2008/254593 |
work_keys_str_mv |
AT ruyunma globalbehaviorofthecomponentsforthesecondordermpointboundaryvalueproblems AT yulianan globalbehaviorofthecomponentsforthesecondordermpointboundaryvalueproblems |
_version_ |
1725344842027892736 |