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

Song-Yue Yu and Baoqiang Yan
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Song-Yue Yu: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Baoqiang Yan: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Mathematics, 2021, vol. 9, issue 17, 1-17

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 ? . Thirdly, the uniqueness of the solution for K ( x ) < 0 is proved, as well as the monotonicity of the solutions on parameter ? . Finally, we obtain some new results for the existence of solutions, and the dependence on the ? for the case K ( x ) is sign-changing.

Keywords: model of thermal explosion; uniqueness; subsolution and supersolution; the comparison principle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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