Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion
| Autor: | Baoqiang Yan, Song-Yue Yu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
General Mathematics
Mathematical analysis MathematicsofComputing_GENERAL uniqueness Monotonic function Nonlinear boundary conditions Elliptic curve TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES model of thermal explosion the comparison principle Computer Science (miscellaneous) QA1-939 Thermal explosion Nonlinear boundary value problem Uniqueness Engineering (miscellaneous) subsolution and supersolution Mathematics |
| Zdroj: | Mathematics, Vol 9, Iss 2173, p 2173 (2021) Mathematics Volume 9 Issue 17 |
| ISSN: | 2227-7390 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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