Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions
We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/782363 |
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| _version_ | 1832566867817922560 |
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| author | Hui Li Libo Wang Minghe Pei |
| author_facet | Hui Li Libo Wang Minghe Pei |
| author_sort | Hui Li |
| collection | DOAJ |
| description | We investigate the existence of solutions and positive solutions
for a nonlinear fourth-order differential equation with integral boundary conditions of the
form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). By using a fixed point theorem due to D.
O'Regan, the existence of solutions and positive solutions for the previous boundary value
problems is obtained. Meanwhile, as applications, some examples are given to illustrate
our results. |
| format | Article |
| id | doaj-art-114c7271ed6841e4ab9d0c002030ec1e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-114c7271ed6841e4ab9d0c002030ec1e2025-02-03T01:02:58ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/782363782363Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary ConditionsHui Li0Libo Wang1Minghe Pei2Department of Mathematics, Beihua University, Jilin City 132013, ChinaDepartment of Mathematics, Beihua University, Jilin City 132013, ChinaDepartment of Mathematics, Beihua University, Jilin City 132013, ChinaWe investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.http://dx.doi.org/10.1155/2013/782363 |
| spellingShingle | Hui Li Libo Wang Minghe Pei Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions Journal of Applied Mathematics |
| title | Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions |
| title_full | Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions |
| title_fullStr | Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions |
| title_full_unstemmed | Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions |
| title_short | Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions |
| title_sort | solvability of a fourth order boundary value problem with integral boundary conditions |
| url | http://dx.doi.org/10.1155/2013/782363 |
| work_keys_str_mv | AT huili solvabilityofafourthorderboundaryvalueproblemwithintegralboundaryconditions AT libowang solvabilityofafourthorderboundaryvalueproblemwithintegralboundaryconditions AT minghepei solvabilityofafourthorderboundaryvalueproblemwithintegralboundaryconditions |