Multiplicity of solutions for a Kirchhoff equation with non‐linearity concave at the origin

We are concerned with the Kirchhoff problem where is a bounded domain with a regular boundary , and , with for and for . Given appropriate conditions on the function , we successfully applied variational methods to establish the existence of multiple solutions, including both a ground state and a nodal solution, for the specified problem, provided that is sufficiently small and for certain values of .