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 |
| Summary: | 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]. |
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| ISSN: | 1072-6691 |