Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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INFINITELY MANY SMALL SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL SOBOLEV AND HARDY EXPONENTS

  • Liang, Sihua (Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, College of Mathematics, Changchun Normal University) ;
  • Zhang, Jihui (Institute of Mathematics, School of Mathematical Science, Nanjing Normal University) ;
  • Fan, Fan (Institute of Mathematics, School of Mathematical Science, Nanjing Normal University)
  • Received : 2009.10.27
  • Accepted : 2009.11.23
  • Published : 2010.09.30
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Abstract

In this paper, we study the following p&q-Laplacian problem with critical Sobolev and Hardy exponents {$-{\Delta}_pu-{\Delta}_qu={\mu}\frac{{\mid}u{\mid}^{p^*(s)-2}u}{{\mid}x{\mid}^s}+{\lambda}f(x,\;u)$, in $\Omega$, u=0, on $\Omega$, where ${\Omega}\;{\subset}\;\mathbb{R}^{\mathbb{N}}$ is a bounded domain and ${\Delta}_ru=div({\mid}{\nabla}u{\mid}^{r-2}{\nabla}u)$ is the r-Laplacian of u. By using the variational method and concentration-compactness principle, we obtain the existence of infinitely many small solutions for above problem which are the complement of previously known results.

Keywords

References

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