Differential Equations and the Method of Upper and Lower Solutions
نویسنده
چکیده
The purpose of this paper is to give an exposition of the method of upper and lower solutions and its usefulness to the study of periodic solutions to differential equations. Some fundamental topics from analysis, such as continuity, differentiation, integration, and uniform convergence, are assumed to be known by the reader. Concepts behind differential equations, initial value problems, and boundary value problems are introduced along with the method of upper and lower solutions, which may be used to establish the existence of periodic solutions. Several theorems will be presented, some of which include proofs. There are several graphs which illustrate the qualitative nature of the solutions of the differential equations, and they were generated using MATLAB. The topics covered in this paper are mostly pulled from existing work and are not claimed to be original.
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