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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |