On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity

Abstract

Abstract A class of perturbed fractional nonlinear systems is studied. The dynamical system possesses two control parameters and a Lipschitz nonlinearity order of p − 1 $p-1$ . The multiplicity of the weak solutions is proved by means of the variational method and by Ricceri critical points theorems. An illustrative example is analyzed in order to highlight the obtained result.

Keywords

• Fractional differential equations
• Riemann–Liouville fractional derivatives
• Variational methods
• Three solutions
• p-Laplacian