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1. On the Space L^{p(x)}(Omega) with unbounded variable exponent $p(x)$ | |||
Liu Duchao | |||
Mathematics 22 December 2008 | |||
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Abstract:Abstract The function space L^{p(x)}(Omega) with unbounded variable exponent, which generalizing the space L^{p(x)}(Omega) with bounded variable exponent, is investigated in this paper. We have defined a norm, investigated some basic properties of it and proved that the space is a Banach function space (and also a Banach space). Some other properties of the space, such as uniform convexity and embedding have also been investigated. As we will see, the properties of L^{p(x)}(Omega) with unbounded variable exponent is more complex than the space with bounded variable exponent. | |||
TO cite this article:Liu Duchao . On the Space L^{p(x)}(Omega) with unbounded variable exponent $p(x)$[OL].[22 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26824 |
2. Three solutions to a class of $p(x)$-Laplace equation based on Nehari skill | |||
Liu Duchao | |||
Mathematics 05 September 2008 | |||
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Abstract:In this paper, we show the existence of at least three nontrivial solutions to the quasilinear elliptic equation-p(x)-Laplacian equation in a smooth bounded domain with nonlinear boundary condition or Dirichlet boundary condition u=0. The method we used here is based on Nehari skills on three sub-manifolds of the space W^{1,p(x)}(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\Omega). | |||
TO cite this article:Liu Duchao . Three solutions to a class of $p(x)$-Laplace equation based on Nehari skill[OL].[ 5 September 2008] http://en.paper.edu.cn/en_releasepaper/content/23823 |
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