Bulletin of the Australian Mathematical
Society
Bull. Austral. Math. Soc.
0004-9727
ALNBAB
2005
72
1
10.wxyz/CV72P1
http://www.austms.org.au/Publ/Bulletin/V72P1/
A new variational method for the $p(x)$-Laplacian
equation
Marek
Galewski
14 February 2006
2006
2
14
53
65
721-5041-Galewski-2005
10.wxyz/C2005V72P1p53
http://www.austms.org.au/Publ/Bulletin/V72P1/721-5041-Galewski/
Using a dual variational method we shall show the
existence of solutions to the Dirichlet problem \begin
{eqnarray} -\divv \Bigl ( \bigl | \nabla u( x) \bigr | ^{p(
x) -2}\nabla u( x) \Bigr ) &=&F_{u}\bigl ( x,u( x)
\bigr ) \text {, }u\in W_{0}^{1,p ( x ) } ( \Omega )
\nonumber \\ x ( y ) | _{\partial \Omega }&=&0. \end
{eqnarray} without assuming Palais--Smale
condition.
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