Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth
In this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with "non-periodic" boundary conditions. These boundary conditions include, as a special case, so-called "anti-perio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2007-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/105/abstr.html |
| _version_ | 1818564270460239872 |
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| author | Christopher C. Tisdell Juan J. Nieto |
| author_facet | Christopher C. Tisdell Juan J. Nieto |
| author_sort | Christopher C. Tisdell |
| collection | DOAJ |
| description | In this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with "non-periodic" boundary conditions. These boundary conditions include, as a special case, so-called "anti-periodic" boundary conditions. Our methods to prove the existence and uniqueness of solutions involve new differential inequalities, the classical fixed-point theorem of Schaefer, and the Nonlinear Alternative. Our new results apply to systems of impulsive differential equations where the right-hand side of the equation may grow linearly, or sub- or super-linearly in its second argument. |
| first_indexed | 2024-12-14T01:26:54Z |
| format | Article |
| id | doaj.art-3ec95edf1b734372bc88156b2072c030 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T01:26:54Z |
| publishDate | 2007-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3ec95edf1b734372bc88156b2072c0302022-12-21T23:22:09ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-07-012007105114Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growthChristopher C. TisdellJuan J. NietoIn this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with "non-periodic" boundary conditions. These boundary conditions include, as a special case, so-called "anti-periodic" boundary conditions. Our methods to prove the existence and uniqueness of solutions involve new differential inequalities, the classical fixed-point theorem of Schaefer, and the Nonlinear Alternative. Our new results apply to systems of impulsive differential equations where the right-hand side of the equation may grow linearly, or sub- or super-linearly in its second argument.http://ejde.math.txstate.edu/Volumes/2007/105/abstr.htmlExistence and uniqueness of solutionsboundary value problemsimpulsive equationsfixed-point theorysystem of equations |
| spellingShingle | Christopher C. Tisdell Juan J. Nieto Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth Electronic Journal of Differential Equations Existence and uniqueness of solutions boundary value problems impulsive equations fixed-point theory system of equations |
| title | Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth |
| title_full | Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth |
| title_fullStr | Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth |
| title_full_unstemmed | Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth |
| title_short | Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth |
| title_sort | existence and uniqueness of solutions to first order systems of nonlinear impulsive boundary value problems with sub super linear or linear growth |
| topic | Existence and uniqueness of solutions boundary value problems impulsive equations fixed-point theory system of equations |
| url | http://ejde.math.txstate.edu/Volumes/2007/105/abstr.html |
| work_keys_str_mv | AT christopherctisdell existenceanduniquenessofsolutionstofirstordersystemsofnonlinearimpulsiveboundaryvalueproblemswithsubsuperlinearorlineargrowth AT juanjnieto existenceanduniquenessofsolutionstofirstordersystemsofnonlinearimpulsiveboundaryvalueproblemswithsubsuperlinearorlineargrowth |