Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications
Let T>2 be an integer and T={1,2,…,T}. We show the existence of the principal eigenvalues of linear periodic eigenvalue problem -Δ2u(j-1)+q(j)u(j)=λg(j)u(j), j∈T, u(0)=u(T), u(1)=u(T+1), and we determine the sign of the corresponding eigenfunctions, where λ is a parameter, q(j)≥0 and q(j)≢0 in...
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Hindawi Limited
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/1949254 |
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doaj-2c2973474cdf4d3fa9af1bfce03de88c2020-11-24T22:37:38ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/19492541949254Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its ApplicationsRuyun Ma0Man Xu1Yan Long2Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaLet T>2 be an integer and T={1,2,…,T}. We show the existence of the principal eigenvalues of linear periodic eigenvalue problem -Δ2u(j-1)+q(j)u(j)=λg(j)u(j), j∈T, u(0)=u(T), u(1)=u(T+1), and we determine the sign of the corresponding eigenfunctions, where λ is a parameter, q(j)≥0 and q(j)≢0 in T, and the weight function g changes its sign in T. As an application of our spectrum results, we use the global bifurcation theory to study the existence of positive solutions for the corresponding nonlinear problem.http://dx.doi.org/10.1155/2018/1949254 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ruyun Ma Man Xu Yan Long |
| spellingShingle |
Ruyun Ma Man Xu Yan Long Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications Discrete Dynamics in Nature and Society |
| author_facet |
Ruyun Ma Man Xu Yan Long |
| author_sort |
Ruyun Ma |
| title |
Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications |
| title_short |
Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications |
| title_full |
Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications |
| title_fullStr |
Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications |
| title_full_unstemmed |
Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications |
| title_sort |
principal eigenvalues of a second-order difference operator with sign-changing weight and its applications |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2018-01-01 |
| description |
Let T>2 be an integer and T={1,2,…,T}. We show the existence of the principal eigenvalues of linear periodic eigenvalue problem -Δ2u(j-1)+q(j)u(j)=λg(j)u(j), j∈T, u(0)=u(T), u(1)=u(T+1), and we determine the sign of the corresponding eigenfunctions, where λ is a parameter, q(j)≥0 and q(j)≢0 in T, and the weight function g changes its sign in T. As an application of our spectrum results, we use the global bifurcation theory to study the existence of positive solutions for the corresponding nonlinear problem. |
| url |
http://dx.doi.org/10.1155/2018/1949254 |
| work_keys_str_mv |
AT ruyunma principaleigenvaluesofasecondorderdifferenceoperatorwithsignchangingweightanditsapplications AT manxu principaleigenvaluesofasecondorderdifferenceoperatorwithsignchangingweightanditsapplications AT yanlong principaleigenvaluesofasecondorderdifferenceoperatorwithsignchangingweightanditsapplications |
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1725716199125286912 |