Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐
Existence and multiplicity of positive solutions for the following semilinear elliptic equation: โฮ๐ข+๐ข=๐(๐ฅ)|๐ข|๐โ2๐ข+๐๐(๐ฅ)|๐ข|๐โ2๐ข in โ๐, ๐ขโ๐ป1(โ๐), are established, where ๐>0,1<๐<2<๐<2โ(2โ=2๐/(๐โ2) if ๐โฅ3,2โ=โ if ๐=1,2), ๐, ๐ satisfy suitable conditions, and ๐ maybe changes sign in โ๐....
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/864296 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562840241700864 |
|---|---|
| author | Tsing-San Hsu |
| author_facet | Tsing-San Hsu |
| author_sort | Tsing-San Hsu |
| collection | DOAJ |
| description | Existence and multiplicity of positive solutions for the following
semilinear elliptic equation: โฮ๐ข+๐ข=๐(๐ฅ)|๐ข|๐โ2๐ข+๐๐(๐ฅ)|๐ข|๐โ2๐ข in โ๐, ๐ขโ๐ป1(โ๐), are established, where ๐>0,1<๐<2<๐<2โ(2โ=2๐/(๐โ2) if ๐โฅ3,2โ=โ
if ๐=1,2), ๐, ๐ satisfy suitable conditions, and ๐ maybe changes sign in โ๐. The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold. |
| format | Article |
| id | doaj-art-c48303b405a44397982fd5296aa0146c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c48303b405a44397982fd5296aa0146c2025-02-03T01:21:45ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/864296864296Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐Tsing-San Hsu0Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, TaiwanExistence and multiplicity of positive solutions for the following semilinear elliptic equation: โฮ๐ข+๐ข=๐(๐ฅ)|๐ข|๐โ2๐ข+๐๐(๐ฅ)|๐ข|๐โ2๐ข in โ๐, ๐ขโ๐ป1(โ๐), are established, where ๐>0,1<๐<2<๐<2โ(2โ=2๐/(๐โ2) if ๐โฅ3,2โ=โ if ๐=1,2), ๐, ๐ satisfy suitable conditions, and ๐ maybe changes sign in โ๐. The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold.http://dx.doi.org/10.1155/2011/864296 |
| spellingShingle | Tsing-San Hsu Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐ Abstract and Applied Analysis |
| title | Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐ |
| title_full | Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐ |
| title_fullStr | Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐ |
| title_full_unstemmed | Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐ |
| title_short | Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in โ๐ |
| title_sort | multiple positive solutions for semilinear elliptic equations with sign changing weight functions in r๐ |
| url | http://dx.doi.org/10.1155/2011/864296 |
| work_keys_str_mv | AT tsingsanhsu multiplepositivesolutionsforsemilinearellipticequationswithsignchangingweightfunctionsinrn |