Electron. J. Diff. Equ., Vol. 2014 (2014), No. 17, pp. 1-22.

Existence of multiple solutions for quasilinear elliptic equations in R^N

Honghui Yin, Zuodong Yang

Abstract:
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].

Submitted August 4, 2013. Published January 10, 2014.
Math Subject Classifications: 35J62, 35J50， 35J92.
Key Words: Nehari manifold; quasilinear; positive solution; (PS)-sequence.

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  Honghui Yin
Institute of Mathematics, School of Mathematical Sciences
Nanjing Normal University
Jiangsu Nanjing 210023, China
email: yinhh771109@163.com
Zuodong Yang
Institute of Mathematics, School of Mathematical Sciences
Nanjing Normal University
Jiangsu Nanjing 210023, China
email: zdyang_jin@263.net

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