Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation
We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equation x′′(t)=f(t,x(ϕ(t))), t∈(0,1), with the nonlocal condition ∑k=1makx(τk)=x0, x′(0)+∑j=1nbjx′(ηj)=x1, where τk∈(a,d)⊂(0,1), ηj∈(c,e)⊂(0,1), and...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/489353 |
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doaj-a4effafd9a1044c180cef387817c5ad72020-11-24T22:54:15ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/489353489353Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential EquationA. M. A. El-Sayed0E. M. Hamdallah1Kh. W. El-kadeky2Faculty of Science, Alexandria University, Alexandria, EgyptFaculty of Science, Alexandria University, Alexandria, EgyptFaculty of Science, Garyounis University, Benghazi, LibyaWe study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equation x′′(t)=f(t,x(ϕ(t))), t∈(0,1), with the nonlocal condition ∑k=1makx(τk)=x0, x′(0)+∑j=1nbjx′(ηj)=x1, where τk∈(a,d)⊂(0,1), ηj∈(c,e)⊂(0,1), and x0,x1>0. As an application the integral and the nonlocal conditions ∫adx(t)dt=x0, x′(0)+x(e)-x(c)=x1 will be considered.http://dx.doi.org/10.1155/2012/489353 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. M. A. El-Sayed E. M. Hamdallah Kh. W. El-kadeky |
| spellingShingle |
A. M. A. El-Sayed E. M. Hamdallah Kh. W. El-kadeky Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation Abstract and Applied Analysis |
| author_facet |
A. M. A. El-Sayed E. M. Hamdallah Kh. W. El-kadeky |
| author_sort |
A. M. A. El-Sayed |
| title |
Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation |
| title_short |
Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation |
| title_full |
Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation |
| title_fullStr |
Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation |
| title_full_unstemmed |
Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation |
| title_sort |
monotonic positive solutions of nonlocal boundary value problems for a second-order functional differential equation |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2012-01-01 |
| description |
We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equation x′′(t)=f(t,x(ϕ(t))), t∈(0,1), with the nonlocal condition ∑k=1makx(τk)=x0, x′(0)+∑j=1nbjx′(ηj)=x1, where τk∈(a,d)⊂(0,1), ηj∈(c,e)⊂(0,1), and x0,x1>0. As an application the integral and the nonlocal conditions ∫adx(t)dt=x0, x′(0)+x(e)-x(c)=x1 will be considered. |
| url |
http://dx.doi.org/10.1155/2012/489353 |
| work_keys_str_mv |
AT amaelsayed monotonicpositivesolutionsofnonlocalboundaryvalueproblemsforasecondorderfunctionaldifferentialequation AT emhamdallah monotonicpositivesolutionsofnonlocalboundaryvalueproblemsforasecondorderfunctionaldifferentialequation AT khwelkadeky monotonicpositivesolutionsofnonlocalboundaryvalueproblemsforasecondorderfunctionaldifferentialequation |
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