Work

Existence of Positive Solutions for Singular Difference Equations with Nonlinear Boundary Conditions

Year: 2024

Type: article

Abstract: In this paper, we delve into a discrete nonlinear singular semipositone problem, characterized by a nonlinear boundary condition. The nonlinearity, given by f(u)−auα with α>0, exhibits a singularity at u=0 and tends towards −∞ as u approaches 0+. By constructing some suitable auxiliary problems, the difficulty that arises from the singularity and semipositone of nonlinearity and the lack of a maximum principle is overcome. Subsequently, employing the Krasnosel’skii fixed-point theorem, we determine the parameter range that ensures the existence of at least one positive solution and the emergence of at least two positive solutions. Furthermore, based on our existence results, one can obtain the symmetry of the solutions after adding some symmetric conditions on the given functions by using a standard argument.

Source: Symmetry

DOI: 10.3390/sym16101313

Authors: Hua Luo, Alhussein Mohamed

Institutions: Shanghai International Studies University, Northwest Normal University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: National Natural Science Foundation of China