Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions
Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions for p-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integ...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/418410 |
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| _version_ | 1832554887622164480 |
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| author | Yan Sun |
| author_facet | Yan Sun |
| author_sort | Yan Sun |
| collection | DOAJ |
| description | Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions for p-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples to demonstrate the main results. |
| format | Article |
| id | doaj-art-115f479e8d02409ea0978379c63e9415 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-115f479e8d02409ea0978379c63e94152025-02-03T05:50:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/418410418410Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral ConditionsYan Sun0Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaUnder some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions for p-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples to demonstrate the main results.http://dx.doi.org/10.1155/2015/418410 |
| spellingShingle | Yan Sun Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions Discrete Dynamics in Nature and Society |
| title | Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions |
| title_full | Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions |
| title_fullStr | Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions |
| title_full_unstemmed | Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions |
| title_short | Positive Solutions for a Class of Fourth-Order p-Laplacian Boundary Value Problem Involving Integral Conditions |
| title_sort | positive solutions for a class of fourth order p laplacian boundary value problem involving integral conditions |
| url | http://dx.doi.org/10.1155/2015/418410 |
| work_keys_str_mv | AT yansun positivesolutionsforaclassoffourthorderplaplacianboundaryvalueprobleminvolvingintegralconditions |