Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems
We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functio...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/364079 |
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| _version_ | 1832549043804307456 |
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| author | Bo Zheng |
| author_facet | Bo Zheng |
| author_sort | Bo Zheng |
| collection | DOAJ |
| description | We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, some new conditions on the existence and multiplicity of solutions are obtained by combining some nonlinear analysis methods, such as Leray-Schauder principle and Morse theory. Our results are new even for the case of asymptotically linear. |
| format | Article |
| id | doaj-art-84f17a673c1a4c4d914a20382b0018c2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-84f17a673c1a4c4d914a20382b0018c22025-02-03T06:12:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/364079364079Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value ProblemsBo Zheng0College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, ChinaWe consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, some new conditions on the existence and multiplicity of solutions are obtained by combining some nonlinear analysis methods, such as Leray-Schauder principle and Morse theory. Our results are new even for the case of asymptotically linear.http://dx.doi.org/10.1155/2010/364079 |
| spellingShingle | Bo Zheng Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems Discrete Dynamics in Nature and Society |
| title | Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems |
| title_full | Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems |
| title_fullStr | Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems |
| title_full_unstemmed | Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems |
| title_short | Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems |
| title_sort | existence and multiplicity of solutions to discrete conjugate boundary value problems |
| url | http://dx.doi.org/10.1155/2010/364079 |
| work_keys_str_mv | AT bozheng existenceandmultiplicityofsolutionstodiscreteconjugateboundaryvalueproblems |