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September/October 2012 Multiple positive solutions for a quasilinear elliptic equation in $\mathbb {R}^N$
Zhaosheng Feng, Zuodong Yang, Honghui Yin
Differential Integral Equations 25(9/10): 977-992 (September/October 2012). DOI: 10.57262/die/1356012378


In this paper, by means of the extraction of the Palais--Smale sequence in the Nehari manifold, we are concerned with the existence of multiple positive solutions of a class of the p-Laplacian equations involving concave-convex nonlinearities $$\left\{ \begin{array}{ll} -\triangle_p u+|u|^{p-2}u=a(x)|u|^{s-2}u +\lambda b(x)|u|^{r-2}u,\;\;\; x\in {\mathbb R}^N,\\ u\in W^{1,p}({\mathbb R}^N), \end{array} \right.$$ in the whole space ${\mathbb R}^N,$ where $\lambda$ is a positive constant, $1\leq r < p < s < p^*=\frac{Np}{N-p}$, and $a(x)$ and $b(x)$ are nonnegative continuous functions in ${\mathbb R}^N.$


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Zhaosheng Feng. Zuodong Yang. Honghui Yin. "Multiple positive solutions for a quasilinear elliptic equation in $\mathbb {R}^N$." Differential Integral Equations 25 (9/10) 977 - 992, September/October 2012.


Published: September/October 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1274.35133
MathSciNet: MR2985690
Digital Object Identifier: 10.57262/die/1356012378

Primary: 35B09 , 35J62 , 35J91

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.25 • No. 9/10 • September/October 2012
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