Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3
We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3|∇u|2dx)Δu+u=k(x)f(u)+h(x), x∈R3, u∈H1(R3), u>0, x∈R3, where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Eke...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/710949 |
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| author | Ling Ding Lin Li Jin-Ling Zhang |
| author_facet | Ling Ding Lin Li Jin-Ling Zhang |
| author_sort | Ling Ding |
| collection | DOAJ |
| description | We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3|∇u|2dx)Δu+u=k(x)f(u)+h(x), x∈R3, u∈H1(R3), u>0, x∈R3, where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. |
| format | Article |
| id | doaj-art-67b3f64415d84aeba53c4e5582237467 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-67b3f64415d84aeba53c4e55822374672025-02-03T01:04:56ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/710949710949Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3Ling Ding0Lin Li1Jin-Ling Zhang2School of Mathematics and Computer Science, Hubei University of Arts and Science, Hubei 441053, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Computer Science, Hubei University of Arts and Science, Hubei 441053, ChinaWe study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3|∇u|2dx)Δu+u=k(x)f(u)+h(x), x∈R3, u∈H1(R3), u>0, x∈R3, where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.http://dx.doi.org/10.1155/2014/710949 |
| spellingShingle | Ling Ding Lin Li Jin-Ling Zhang Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 Abstract and Applied Analysis |
| title | Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 |
| title_full | Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 |
| title_fullStr | Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 |
| title_full_unstemmed | Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 |
| title_short | Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 |
| title_sort | positive solutions for a nonhomogeneous kirchhoff equation with the asymptotical nonlinearity in r3 |
| url | http://dx.doi.org/10.1155/2014/710949 |
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