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We give an upper bound for the least energy of a sign-changing solution tothe the nonlinear scalar field equation $$-\Delta u = f(u), \qquad u\inD^{1,2}(\mathbb{R}^{N}),$$ where $N\geq5$ and the nonlinearity $f$ issubcritical at infinity and supercritical near the origin. More precisely, weestablish the existence of a nonradial sign-changing solution whose energy issmaller that $12c_0$ if $N=5,6$ and smaller than $10c_0$ if $N\geq 7$, where$c_0$ is the ground state energy.

An upper bound for the least energy of a sign-changing solution to a zero mass problem