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Volume 9
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Article

Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion

by
Song-Yue Yu
and
Baoqiang Yan
*
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(17), 2173; https://doi.org/10.3390/math9172173
Submission received: 7 August 2021 / Revised: 2 September 2021 / Accepted: 2 September 2021 / Published: 6 September 2021
(This article belongs to the Special Issue Nonlinear Boundary Value Problems and Their Applications)
Versions Notes

Abstract

In this paper, the thermal explosion model described by a nonlinear boundary value problem is studied. Firstly, we prove the comparison principle under nonlinear boundary conditions. Secondly, using the sub-super solution theorem, we prove the existence of a positive solution for the case K(x)>0, as well as the monotonicity of the maximal solution on parameter λ. Thirdly, the uniqueness of the solution for K(x)<0 is proved, as well as the monotonicity of the solutions on parameter λ. Finally, we obtain some new results for the existence of solutions, and the dependence on the λ for the case K(x) is sign-changing.
Keywords: model of thermal explosion; uniqueness; subsolution and supersolution; the comparison principle model of thermal explosion; uniqueness; subsolution and supersolution; the comparison principle

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MDPI and ACS Style

Yu, S.-Y.; Yan, B. Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion. Mathematics 2021, 9, 2173. https://doi.org/10.3390/math9172173

AMA Style

Yu S-Y, Yan B. Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion. Mathematics. 2021; 9(17):2173. https://doi.org/10.3390/math9172173

Chicago/Turabian Style

Yu, Song-Yue, and Baoqiang Yan. 2021. "Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion" Mathematics 9, no. 17: 2173. https://doi.org/10.3390/math9172173

APA Style

Yu, S.-Y., & Yan, B. (2021). Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion. Mathematics, 9(17), 2173. https://doi.org/10.3390/math9172173

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