Kirchhoff Equation with New Local Sublinear Nonlinearities

In this paper, we investigate the existence of infinitely many solutions to the following nonlinear Kirchhoff-type equation: -(1+b∫_R³(|∇ u|²+V(x)u²)\,dx)[Δ u+V(x)u]=f(x,u) \ \ R³, where $$b>0$$ is a constant, $$V(x)$$ is a nonnegative potential, and the nonlinearity $$f(x,u)$$ satisfies certain new local sublinear conditions. Using variational methods and a symmetric version of the mountain pass theorem, we establish the existence of infinitely many weak solutions. Several examples are provided to illustrate the applicability of our main results.