Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞
We study the existence of nodal solutions for the following problem: -x″=αx++βx-+ra(t)f(x), 0<t<1, x(0)=x(1)=0, where r≠0 is a parameter, a(t)∈C([0,1],(0,∞)) with a(t)≢0 on any subinterval of [0,1], x+=max{x,0},x-=-min{x,0}, and α,β∈C[0,1]; f∈C(R,R), sf(s)>0 for s≠0, and f0,f∞∉(0,∞), where...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/2386287 |
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| author | Wenguo Shen |
| author_facet | Wenguo Shen |
| author_sort | Wenguo Shen |
| collection | DOAJ |
| description | We study the existence of nodal solutions for the following problem: -x″=αx++βx-+ra(t)f(x), 0<t<1, x(0)=x(1)=0, where r≠0 is a parameter, a(t)∈C([0,1],(0,∞)) with a(t)≢0 on any subinterval of [0,1], x+=max{x,0},x-=-min{x,0}, and α,β∈C[0,1]; f∈C(R,R), sf(s)>0 for s≠0, and f0,f∞∉(0,∞), where f0=lim|s|→0f(s)/s and f∞=lim|s|→+∞f(s)/s. We use bifurcation techniques to prove our main results. |
| format | Article |
| id | doaj-art-e4f8c2887feb42fc96f64091141fcc10 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e4f8c2887feb42fc96f64091141fcc102025-02-03T01:12:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/23862872386287Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞Wenguo Shen0Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, ChinaWe study the existence of nodal solutions for the following problem: -x″=αx++βx-+ra(t)f(x), 0<t<1, x(0)=x(1)=0, where r≠0 is a parameter, a(t)∈C([0,1],(0,∞)) with a(t)≢0 on any subinterval of [0,1], x+=max{x,0},x-=-min{x,0}, and α,β∈C[0,1]; f∈C(R,R), sf(s)>0 for s≠0, and f0,f∞∉(0,∞), where f0=lim|s|→0f(s)/s and f∞=lim|s|→+∞f(s)/s. We use bifurcation techniques to prove our main results.http://dx.doi.org/10.1155/2016/2386287 |
| spellingShingle | Wenguo Shen Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ Discrete Dynamics in Nature and Society |
| title | Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ |
| title_full | Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ |
| title_fullStr | Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ |
| title_full_unstemmed | Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ |
| title_short | Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ |
| title_sort | bifurcation and nodal solutions for the half linear problems with nonasymptotic nonlinearity at 0 and ∞ |
| url | http://dx.doi.org/10.1155/2016/2386287 |
| work_keys_str_mv | AT wenguoshen bifurcationandnodalsolutionsforthehalflinearproblemswithnonasymptoticnonlinearityat0and |