IJPAM: Volume 47, No. 3 (2008)

MULTIPLE SOLUTIONS FOR ELLIPTIC EQUATIONS
WITH NONSTANDARD GROWTH CONDITIONS

Xiayang Shi$^1$, Yuqi Niu$^2$, Xuanhao Ding$^3$, Yingchun Jiang$^4$
$^{1,3,4}$School of Mathematics and Computational Science
Guilin University of Electronical Technology
Guilin, 541004, P.R. CHINA
$^1$e-mail: aryang123@163.com
$^3$e-mail: dxuanhao@ctbu.edu.cn
$^4$e-mail: jiang2007@guet.edu.cn
$^2$School of Mathematical Science
Xuchang University
Xuchang, 461000, P.R. CHINA
e-mail: niuyuqi003@126.com


Abstract.In this paper, we investigate the existence and multiplicity of solutions for $p(x)$-Laplacian Dirichlet problem with nonstandard growth conditions by using the Ricceri variational principle. We verify the equation has at least three solution and obtain generalizes the corresponding result

Received: June 26, 2008

AMS Subject Classification: 46T30, 47H07

Key Words and Phrases: $p(x)$-Laplacian, variable exponent, Sobolev space, Ricceri's variational principle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 3