Existence of Solutions for Kirchhoff-Type Fractional Dirichlet Problem with <i>p</i>-Laplacian

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 <i>p</i>-laplacian
• local superquadratic nonlinearity
• mountain pass theorem
• existence