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Numerical Analysis and Applicable Mathematics

Research Article

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. 

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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

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Cited By

This article is cited by 1 publication.

  1. Fečkan, M., Li, Q. and Wang, J., 2022. Existence and Ulam-Hyers stability of positive solutions for a nonlinear model for the Antarctic Circumpolar Current. Monatshefte für Mathematik, 197(3), pp.419-434. [CrossRef]