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

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 lambda. By mountain pass theorem, we obtain that system has at least one non-trivial weak solution u lambda under some local conditions for each given large parameter lambda. We get a concrete lower bound of the parameter lambda, and then obtain two estimates of weak solutions u lambda. We also obtain that u lambda -> 0 if lambda tends to infinity. Finally, we present an example as an application of our results.