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

Danyang Kang, Cuiling Liu and Xingyong Zhang
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Danyang Kang: Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
Cuiling Liu: Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
Xingyong Zhang: Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China

Mathematics, 2020, vol. 8, issue 1, 1-17

Abstract: 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.

Keywords: Kirchhoff-type system; fractional p -Laplacian; local superquadratic nonlinearity; mountain pass theorem; existence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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