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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Song-Yue Yu & Baoqiang Yan, 2021. "Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion," Mathematics, MDPI, vol. 9(17), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2173-:d:629722
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    Cited by:

    1. Songyue Yu & Baoqiang Yan, 2022. "Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations," Mathematics, MDPI, vol. 10(12), pages 1-19, June.

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