非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0)
We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x""+kx" +lx = λh(t）x+g(t, x，λ），0<t<1,x(0) = x(1) =x'(0)=x'(1）=0. Under some natural hypotheses on the perturbation function g: (0,1) ×R2 →R, we sh...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Zhejiang University Press
2016-09-01
|
| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2016.05.005 |
| _version_ | 1797235796643676160 |
|---|---|
| author | SHENWenguo(沈文国) |
| author_facet | SHENWenguo(沈文国) |
| author_sort | SHENWenguo(沈文国) |
| collection | DOAJ |
| description | We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x""+kx" +lx = λh(t）x+g(t, x，λ），0<t<1,x(0) = x(1) =x'(0)=x'(1）=0. Under some natural hypotheses on the perturbation function g: (0,1) ×R2 →R, we show that （λk，0） is a bifurcation point of the above problem. And there are two distinct unbounded continuas, and ,consisting of the bifurcation branch Ck from （λk，0），where λk is the k-th eigenvalue of the linear problem corresponding to the above problems. As an application of the above result,the global behavior of the components of nodal solutions of the following problem x"" + kx" +lx = rh(t) f(x) , 0<t<1， x(0)=x(1)=x'(0) = x'(1)=0 is studied. We obtain the existence of multiple nodal solutions for the problem if f0 =∞, f∞ ∈ （0，∞），. |
| first_indexed | 2024-04-24T16:53:39Z |
| format | Article |
| id | doaj.art-516ee0bea2bb4a53834c02289d9c1b22 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:53:39Z |
| publishDate | 2016-09-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-516ee0bea2bb4a53834c02289d9c1b222024-03-29T01:58:36ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972016-09-0143552553110.3785/j.issn.1008-9497.2016.05.005非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0)SHENWenguo(沈文国)0https://orcid.org/0000-0001-7323-1887(Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050,China)We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x""+kx" +lx = λh(t）x+g(t, x，λ），0<t<1,x(0) = x(1) =x'(0)=x'(1）=0. Under some natural hypotheses on the perturbation function g: (0,1) ×R2 →R, we show that （λk，0） is a bifurcation point of the above problem. And there are two distinct unbounded continuas, and ,consisting of the bifurcation branch Ck from （λk，0），where λk is the k-th eigenvalue of the linear problem corresponding to the above problems. As an application of the above result,the global behavior of the components of nodal solutions of the following problem x"" + kx" +lx = rh(t) f(x) , 0<t<1， x(0)=x(1)=x'(0) = x'(1)=0 is studied. We obtain the existence of multiple nodal solutions for the problem if f0 =∞, f∞ ∈ （0，∞），.https://doi.org/10.3785/j.issn.1008-9497.2016.05.005fourth-order problemsunilateral global bifurcationnodal solutionsnon-asymptotic non-linearity at 0 |
| spellingShingle | SHENWenguo(沈文国) 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0) Zhejiang Daxue xuebao. Lixue ban fourth-order problems unilateral global bifurcation nodal solutions non-asymptotic non-linearity at 0 |
| title | 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0) |
| title_full | 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0) |
| title_fullStr | 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0) |
| title_full_unstemmed | 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0) |
| title_short | 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧(Unilateral global bifurcation for fourth-order boundary value problem with non-asymptotic nonlinearity at 0) |
| title_sort | 非线性项在零点非渐进增长的四阶边值问题单侧全局分歧 unilateral global bifurcation for fourth order boundary value problem with non asymptotic nonlinearity at 0 |
| topic | fourth-order problems unilateral global bifurcation nodal solutions non-asymptotic non-linearity at 0 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2016.05.005 |
| work_keys_str_mv | AT shenwenguoshěnwénguó fēixiànxìngxiàngzàilíngdiǎnfēijiànjìnzēngzhǎngdesìjiēbiānzhíwèntídāncèquánjúfēnqíunilateralglobalbifurcationforfourthorderboundaryvalueproblemwithnonasymptoticnonlinearityat0 |