Positive ground state solution for Kirchhoff equations with subcritical growth and zero mass
In this article, we study the Kirchhoff equation $$\displaylines{ -\Big(a+b\int_{\mathbb{R}^N}|\nabla u|^{2}dx\Big)\Delta u=K(x)f(u), \quad x\in \mathbb{R}^N,\cr u\in D^{1,2}(\mathbb{R}^N), }$$ where a>0, b>0 and $N\geq3$. Under suitable conditions on K and f, we obtain four existence...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/262/abstr.html |
| Summary: | In this article, we study the Kirchhoff equation
$$\displaylines{
-\Big(a+b\int_{\mathbb{R}^N}|\nabla u|^{2}dx\Big)\Delta u=K(x)f(u), \quad
x\in \mathbb{R}^N,\cr
u\in D^{1,2}(\mathbb{R}^N),
}$$
where a>0, b>0 and $N\geq3$. Under suitable conditions on K and f,
we obtain four existence results and two nonexistence results, using
variational methods. |
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| ISSN: | 1072-6691 |