Existence of multiple solutions for quasilinear elliptic equations in R^N
In this article, we establish the multiplicity of positive weak solution for the quasilinear elliptic equation $$\displaylines{ -\Delta_p u+\lambda|u|^{p-2}u=f(x) |u|^{s-2 }u+h(x)|u|^{r-2}u\quad x\in \mathbb{R}^N,\cr u>0\quad x\in \mathbb{R}^N,\cr u\in W^{1,p}(\mathbb{R}^N) }$$ We sho...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/17/abstr.html |
| _version_ | 1818265174761537536 |
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| author | Honghui Yin Zuodong Yang |
| author_facet | Honghui Yin Zuodong Yang |
| author_sort | Honghui Yin |
| collection | DOAJ |
| description | In this article, we establish the multiplicity of positive weak solution for
the quasilinear elliptic equation
$$\displaylines{
-\Delta_p u+\lambda|u|^{p-2}u=f(x) |u|^{s-2 }u+h(x)|u|^{r-2}u\quad
x\in \mathbb{R}^N,\cr
u>0\quad x\in \mathbb{R}^N,\cr
u\in W^{1,p}(\mathbb{R}^N)
}$$
We show how the shape of the graph of f affects the number of
positive solutions. Our results extend the corresponding results
in [21]. |
| first_indexed | 2024-12-12T19:46:37Z |
| format | Article |
| id | doaj.art-2609a65ad0f94520a93d0e25010fdadb |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T19:46:37Z |
| publishDate | 2014-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-2609a65ad0f94520a93d0e25010fdadb2022-12-22T00:14:03ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-01-01201417,122Existence of multiple solutions for quasilinear elliptic equations in R^NHonghui Yin0Zuodong Yang1 Huaiyin Normal Univ., Jiangsu Huaian, China Huaiyin Normal Univ., Jiangsu Huaian, China In this article, we establish the multiplicity of positive weak solution for the quasilinear elliptic equation $$\displaylines{ -\Delta_p u+\lambda|u|^{p-2}u=f(x) |u|^{s-2 }u+h(x)|u|^{r-2}u\quad x\in \mathbb{R}^N,\cr u>0\quad x\in \mathbb{R}^N,\cr u\in W^{1,p}(\mathbb{R}^N) }$$ We show how the shape of the graph of f affects the number of positive solutions. Our results extend the corresponding results in [21].http://ejde.math.txstate.edu/Volumes/2014/17/abstr.htmlNehari manifoldquasilinearpositive solution(PS)-sequence |
| spellingShingle | Honghui Yin Zuodong Yang Existence of multiple solutions for quasilinear elliptic equations in R^N Electronic Journal of Differential Equations Nehari manifold quasilinear positive solution (PS)-sequence |
| title | Existence of multiple solutions for quasilinear elliptic equations in R^N |
| title_full | Existence of multiple solutions for quasilinear elliptic equations in R^N |
| title_fullStr | Existence of multiple solutions for quasilinear elliptic equations in R^N |
| title_full_unstemmed | Existence of multiple solutions for quasilinear elliptic equations in R^N |
| title_short | Existence of multiple solutions for quasilinear elliptic equations in R^N |
| title_sort | existence of multiple solutions for quasilinear elliptic equations in r n |
| topic | Nehari manifold quasilinear positive solution (PS)-sequence |
| url | http://ejde.math.txstate.edu/Volumes/2014/17/abstr.html |
| work_keys_str_mv | AT honghuiyin existenceofmultiplesolutionsforquasilinearellipticequationsinrn AT zuodongyang existenceofmultiplesolutionsforquasilinearellipticequationsinrn |