Bull. Austral. Math. Soc. 72(1) pp.53--65, 2005.

A new variational method for the p(x)-Laplacian equation

Marek Galewski
Received: 9th February, 2005

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Abstract

Using a dual variational method we shall show the existence of solutions to the Dirichlet problem
  -div$\displaystyle \Bigl ($$\displaystyle \bigl \vert $$\displaystyle \nabla $u(x)$\displaystyle \bigr \vert ^{{p( x) -2}}_{}$$\displaystyle \nabla $u(x)$\displaystyle \Bigr )$ = Fu $\displaystyle \bigl ($x, u(x)$\displaystyle \bigr )$, u $\displaystyle \in $ W01, p(x)($\displaystyle \Omega $)
(1) x(y)|$\scriptstyle \partial $$\scriptstyle \Omega $ = 0.

without assuming Palais-Smale condition.

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(Metadata: XML, RSS, BibTeX) MathSciNet: MR2162294 Z'blatt-MATH: 02212186

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