Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters
The author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u, 0<t<1, t≠tk, Δu|t=tk=μIktk, utk, Δu′|t=tk=0, k=1,2,…,n, au(0)-bu′(0)=∫01g(t)u(t)dt,u′(1)=0, where λ>0 and μ>0 are two parameters. Using fixed point theories, se...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/534787 |
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| author | Meiqiang Feng |
| author_facet | Meiqiang Feng |
| author_sort | Meiqiang Feng |
| collection | DOAJ |
| description | The author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u, 0<t<1, t≠tk, Δu|t=tk=μIktk, utk, Δu′|t=tk=0, k=1,2,…,n, au(0)-bu′(0)=∫01g(t)u(t)dt,u′(1)=0, where λ>0 and μ>0 are two parameters. Using fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values of λ>0 and μ>0. The exact upper and lower bounds for these positive solutions are also given. Moreover, the approach to deal with the impulsive term is different from earlier approaches. In this paper, our results cover equations without impulsive effects and are compared with some recent results by Ding and Wang. |
| format | Article |
| id | doaj-art-23e7a2c2bd604e688319a1609bf418ab |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-23e7a2c2bd604e688319a1609bf418ab2025-08-20T02:04:13ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/534787534787Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two ParametersMeiqiang Feng0School of Applied Science, Beijing Information Science & Technology University, Beijing, 100192, ChinaThe author considers an impulsive boundary value problem involving the one-dimensional p-Laplacian -(φp (u′))′=λωtft,u, 0<t<1, t≠tk, Δu|t=tk=μIktk, utk, Δu′|t=tk=0, k=1,2,…,n, au(0)-bu′(0)=∫01g(t)u(t)dt,u′(1)=0, where λ>0 and μ>0 are two parameters. Using fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values of λ>0 and μ>0. The exact upper and lower bounds for these positive solutions are also given. Moreover, the approach to deal with the impulsive term is different from earlier approaches. In this paper, our results cover equations without impulsive effects and are compared with some recent results by Ding and Wang.http://dx.doi.org/10.1155/2014/534787 |
| spellingShingle | Meiqiang Feng Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters Abstract and Applied Analysis |
| title | Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters |
| title_full | Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters |
| title_fullStr | Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters |
| title_full_unstemmed | Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters |
| title_short | Positive Solutions for a Second-Order p-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters |
| title_sort | positive solutions for a second order p laplacian boundary value problem with impulsive effects and two parameters |
| url | http://dx.doi.org/10.1155/2014/534787 |
| work_keys_str_mv | AT meiqiangfeng positivesolutionsforasecondorderplaplacianboundaryvalueproblemwithimpulsiveeffectsandtwoparameters |