2007
DOI: 10.1016/j.jmaa.2006.07.093
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On the sub-supersolution method for p(x)-Laplacian equations

Abstract: This paper deals with the sub-supersolution method for the p(x)-Laplacian equations. A sub-supersolution principle for the Dirichlet problems involving the p(x)-Laplacian is established. It is proved that the local minimizers in the C 1 topology are also local minimizers in the W 1,p(x) topology for given energy functionals. A strong comparison theorem for the p(x)-Laplacian equations is presented. Some applications of the abstract theorems obtained in this paper to the eigenvalue problems for the p(x)-Laplaci… Show more

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Cited by 141 publications
(9 citation statements)
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References 27 publications
(53 reference statements)
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“…In Refs. [7][8][9][10][11][12], Fan et al studied the regularity of solutions for differential equations with nonstandard p(x)-growth conditions.…”
Section: Introductionmentioning
confidence: 99%
“…In Refs. [7][8][9][10][11][12], Fan et al studied the regularity of solutions for differential equations with nonstandard p(x)-growth conditions.…”
Section: Introductionmentioning
confidence: 99%
“…In this article we will use the following sub-supersolution principle, the proof of which is based on the well known fixed point theorem for the increasing operator on the order interval (see e.g., [45]) and is similar to that given in [12] for Dirichlet problems involving the p(x)-Laplacian. …”
Section: Proof According To Propositions 23 and 24 (F V) := F (mentioning
confidence: 99%
“…The variable nonlinearity is used to outline the borders of the true image and to eliminate possible noise. We refer the reader to [7][8][9][10][11] for an overview of and references on this subject, and to [12][13][14][15][16] for the study of the variable exponent equations and the corresponding variational problems.…”
Section: Introductionmentioning
confidence: 99%
“…The study of various mathematical problems with variable exponent are interesting in applications and raise many difficult mathematical problems. We refer the readers to [17][18][19][20][21][22][23] for the study of p(x)-Laplacian equations and the corresponding variational problems. Corrêa and Figueiredo [13] presented several sufficient conditions for the existence of positive solutions to a class of nonlocal boundary value problems of the p-Kirchhoff type equation.…”
Section: Introductionmentioning
confidence: 99%