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Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p-Laplacian

1
Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
2
School of Mathematics and Statistics, Central South University, Changsha 410083, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 106; https://doi.org/10.3390/math8010106
Received: 12 December 2019 / Revised: 2 January 2020 / Accepted: 4 January 2020 / Published: 8 January 2020
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)
In this paper, we investigate the existence of solutions for a class of p-Laplacian fractional order Kirchhoff-type system with Riemann–Liouville fractional derivatives and a parameter λ . By mountain pass theorem, we obtain that system has at least one non-trivial weak solution u λ under some local conditions for each given large parameter λ . We get a concrete lower bound of the parameter λ , and then obtain two estimates of weak solutions u λ . We also obtain that u λ 0 if λ tends to . Finally, we present an example as an application of our results. View Full-Text
Keywords: Kirchhoff-type system; fractional p-Laplacian; local superquadratic nonlinearity; mountain pass theorem; existence Kirchhoff-type system; fractional p-Laplacian; local superquadratic nonlinearity; mountain pass theorem; existence
MDPI and ACS Style

Kang, D.; Liu, C.; Zhang, X. Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with p-Laplacian. Mathematics 2020, 8, 106.

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