Numerical Analysis and Applicable Mathematics
Title
Study of Differential Equations with Exponential Nonlinearities via the Lower and Upper Solutions’ Method
Authors
Michal Feckan*a,b and Kateryna Marynetsc
aDepartment of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská
dolina, 842 48 Bratislava, Slovakia.
bMathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia.
cDelft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science,
Delft University of Technology, Van Mourik Broekmanweg 6, 2628 XE Delft, The Netherlands.
*Corresponding author E-mail address: michal.feckan@fmph.uniba.sk (Michal Feckan)
Article History
Publication details: Received: 21st April 2020; Revised: 27th June 2020; Accepted: 28th June 2020; Published: 08th July 2020
Cite this article
Feckan M.; Marynets K. Study of Differential Equations with Exponential Nonlinearities via the Lower and Upper Solutions’ Method. Numer. Anal. Appl. Math., 2020, 1(2), 1-7.
Abstract
We present original results in study of the second-order differential equation with exponential nonlinearities, subjected to the Dirichlet boundary conditions. Using the proper substitution techniques, we reduce the given problem to the study of its lower and upper solutions.
Keywords
lower and upper solutions; nonlinear boundary-value problem; monotone method; exponential nonlinearity; Dirichlet boundary conditions