Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

Sylwia Barnaś

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2014)

  • Volume: 34, Issue: 1, page 15-39
  • ISSN: 1509-9407

Abstract

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In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

How to cite

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Sylwia Barnaś. "Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 34.1 (2014): 15-39. <http://eudml.org/doc/270445>.

@article{SylwiaBarnaś2014,
abstract = {In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.},
author = {Sylwia Barnaś},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {p(x)-Laplacian; hemivariational inequality; Cerami condition; mountain pass theorem; variable exponent Sobolev space; -Laplacian; variable exponent; Sobolev space},
language = {eng},
number = {1},
pages = {15-39},
title = {Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian},
url = {http://eudml.org/doc/270445},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Sylwia Barnaś
TI - Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2014
VL - 34
IS - 1
SP - 15
EP - 39
AB - In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.
LA - eng
KW - p(x)-Laplacian; hemivariational inequality; Cerami condition; mountain pass theorem; variable exponent Sobolev space; -Laplacian; variable exponent; Sobolev space
UR - http://eudml.org/doc/270445
ER -

References

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