, and the second one is a generalization of the problems studied in. The first problem was derived from a chemical reaction by Aris R. Then, we focus our attention on two specific problems of DBVP (1) for and. In this paper, we study DBVP ( 1) generally first and then develop a schema that can be used to determine the exact number of positive solutions of DBVP ( 1). In recent years, there has been considerable work on the study of the number of positive solutions and bifurcation diagrams of various special cases of the following Dirichlet boundary value problem (DBVP). IntroductionĪs is well known, Dirichlet boundary value problems have a variety of applications in physics, chemistry, and mathematics. Our code in Mathematica is available upon request. We also computed the graphs for some special cases of the second problem, and the results are consistent with the existing results. For the second problem, we determine its number of positive solutions and find a formula for the value of that separates the regions of, in which the problem has different numbers of solutions. We prove first that all positive solutions of the first problem are less than or equal to, obtain more specific lower and upper bounds for these solutions, and compute a curve in the -plane with accuracy up to, below which the first problem has a unique positive solution and above which it has exactly three positive solutions.
Then, we focus our attention on the special cases when and, respectively. We study the Dirichlet boundary value problem generally and develop a schema for determining the relationship between the values of its parameters and the number of positive solutions.
0 kommentar(er)
