Eigenvalue problems for a class of nonlinear Hadamard fractional differential equations with p-Laplacian operator

This paper is concerned with the existence and nonexistence of positive solutions for the eigenvalue problems of nonlinear Hadamard fractional differential equations with -Laplacian operator. By applying the properties of the Green function and Guo-Krasnosel’skii fixed point theorem on cones, some e...

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Bibliographic Details
Published inMathematica Slovaca Vol. 70; no. 1; pp. 107 - 124
Main Author Yang, Wengui
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 01.02.2020
Walter de Gruyter GmbH
Subjects
34A34
Cones
Differential equations
eigenvalue problems
Eigenvalues
Existence theorems
fixed point theorem on cones
Fixed points (mathematics)
Green's functions
Hadamard fractional differential equations
Laplace transforms
Mathematical analysis
Operators (mathematics)
positive solutions
Primary 34B18
Secondary 26A33
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Summary:This paper is concerned with the existence and nonexistence of positive solutions for the eigenvalue problems of nonlinear Hadamard fractional differential equations with -Laplacian operator. By applying the properties of the Green function and Guo-Krasnosel’skii fixed point theorem on cones, some existence and nonexistence results of positive solutions are obtained based on different eigenvalue intervals. Finally, some examples are presented to demonstrate the feasibility of our main results.
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2017-0336