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On the Spaces L and W
Xianling Fan,Dun Zhao +1 more
- 01 Jan 2001
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About: The article was published on 01 Jan 2001. and is currently open access.
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Citations
Existence and multiplicity of solutions for the nonlocal p(x)-Laplacian equations in $R^N$
TL;DR: In this article, the nonlocal p(x)-Laplacian equations in R N with nonvariational form ( A(u) − � p(ex) u + j uj p(ax)−2 u � = B(u),f(x, u) in R n, u 2 W 1,p(x) (R N ), and with the variational form 8 > > >> a � Z RN jr ujp(ex), + j Uj p
On a pure traction problem for the nonlinear elasticity system in Sobolev spaces with variable exponents
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1
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Some Applications to Lebesgue Points in Variable Exponent Lebesgue Spaces
TL;DR: In this paper, some corollaries of Lebesgue's regular points which are useful in the theory of optimal control for distributed parameter systems are proved and used for optimal control of distributed systems.
Existence of solutions for a differential inclusion problem with singular coefficients involving the p(x)-Laplacian
Guowei Dai,Ruyun Ma,Qiaozhen Ma +2 more
TL;DR: Using the non-smooth critical point theory, this article investigated the existence and multiplicity of solutions for a differential inclusion problem with singular coefficients involving the p(x)-Laplacian.
Existence, multiplicity and numerical examples for Schrödinger systems with nonstandard p ( x )-growth conditions
Thiziri Chergui,Saadia Tas +1 more
TL;DR: In this article, a quasi-Newton minimization approach is proposed for discretization of finite elements of the p(x)-Laplacian, which is based on variational inequalities.
1
References
•Book
Orlicz Spaces and Modular Spaces
Julian Musielak
- 01 Nov 1983
TL;DR: In this paper, a family of modulars depending on a parameter is described, and some applications of modular spaces are discussed, including orlicz spaces and countably modulared spaces.
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Averaging of functionals of the calculus of variations and elasticity theory
TL;DR: In this paper, the authors developed a duality method in the theory of averaging of nonlinear variational problems with stochastic Lagrangians and derived duality formulas that take account of the regularity problem.
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