Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations
A class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution and the minimum positive solution was explored. Fu...
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2024-11-01
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| author | Lin-Lin Wang Jing-Jing Liu Yong-Hong Fan |
| author_facet | Lin-Lin Wang Jing-Jing Liu Yong-Hong Fan |
| author_sort | Lin-Lin Wang |
| collection | DOAJ |
| description | A class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution and the minimum positive solution was explored. Furthermore, the uniqueness of the positive solution and its asymptotic estimation at the origin were evaluated. The results show that the asymptotic estimation is similar to that of the corresponding boundary blowup problems. Compared with the conclusions of Wei’s work in 2017, the asymptotic behavior of the solution only depends on the asymptotic behavior of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula> at the origin and the asymptotic behavior of <i>g</i> at infinity. |
| format | Article |
| id | doaj-art-6f8f1d47ba794bd2a448d423496bab7c |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6f8f1d47ba794bd2a448d423496bab7c2025-08-20T02:04:54ZengMDPI AGMathematics2227-73902024-11-011222362410.3390/math12223624Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic EquationsLin-Lin Wang0Jing-Jing Liu1Yong-Hong Fan2School of Mathematics and Statistics Sciences, Ludong University, Yantai 264025, ChinaSchool of Mathematics and Statistics Sciences, Ludong University, Yantai 264025, ChinaSchool of Mathematics and Statistics Sciences, Ludong University, Yantai 264025, ChinaA class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution and the minimum positive solution was explored. Furthermore, the uniqueness of the positive solution and its asymptotic estimation at the origin were evaluated. The results show that the asymptotic estimation is similar to that of the corresponding boundary blowup problems. Compared with the conclusions of Wei’s work in 2017, the asymptotic behavior of the solution only depends on the asymptotic behavior of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula> at the origin and the asymptotic behavior of <i>g</i> at infinity.https://www.mdpi.com/2227-7390/12/22/3624semilinear elliptic differential equationupper and lower solutionblowup problemuniquenessasymptotic behavior |
| spellingShingle | Lin-Lin Wang Jing-Jing Liu Yong-Hong Fan Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations Mathematics semilinear elliptic differential equation upper and lower solution blowup problem uniqueness asymptotic behavior |
| title | Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations |
| title_full | Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations |
| title_fullStr | Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations |
| title_full_unstemmed | Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations |
| title_short | Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations |
| title_sort | existence uniqueness and asymptotic behavior of solutions for semilinear elliptic equations |
| topic | semilinear elliptic differential equation upper and lower solution blowup problem uniqueness asymptotic behavior |
| url | https://www.mdpi.com/2227-7390/12/22/3624 |
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