Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach
We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/375634 |
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| _version_ | 1832555969137082368 |
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| author | Panos K. Palamides Alex P. Palamides |
| author_facet | Panos K. Palamides Alex P. Palamides |
| author_sort | Panos K. Palamides |
| collection | DOAJ |
| description | We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field. |
| format | Article |
| id | doaj-art-0c9d2f99e8354c72900fa465e747dec4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0c9d2f99e8354c72900fa465e747dec42025-02-03T05:46:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/375634375634Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel ApproachPanos K. Palamides0Alex P. Palamides1Naval Academy of Greece, 45110 Piraeus, GreeceTechnological Educational Institute of Piraeus, Department of Electronic Computer Systems, P.Ralli and Thivon 250, 12240 Athens, GreeceWe investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field.http://dx.doi.org/10.1155/2012/375634 |
| spellingShingle | Panos K. Palamides Alex P. Palamides Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach International Journal of Mathematics and Mathematical Sciences |
| title | Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach |
| title_full | Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach |
| title_fullStr | Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach |
| title_full_unstemmed | Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach |
| title_short | Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach |
| title_sort | fourth order four point boundary value problem a solutions funnel approach |
| url | http://dx.doi.org/10.1155/2012/375634 |
| work_keys_str_mv | AT panoskpalamides fourthorderfourpointboundaryvalueproblemasolutionsfunnelapproach AT alexppalamides fourthorderfourpointboundaryvalueproblemasolutionsfunnelapproach |