Existence of Weak Solutions for Nonlinear Time-Fractional p-Laplace Problems

The existence of weak solution for p-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2014-01, Vol.2014 (2014), p.461-469-143
Main Authors: Qiu, Meilan, Mei, Liquan
Format: Article
Language:English
Subjects:
Differential equations, Nonlinear
Existence theorems
Fixed point theory
Imbeddings
Laplacian operator
Manifolds
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical research
Nonlinearity
Optimization
Sequences
Theorems
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Summary:The existence of weak solution for p-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is established. By means of the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations of the p-Laplace problem are obtained.
ISSN:1110-757X
1687-0042
DOI:10.1155/2014/231892