On radially symmetric solutions of the Neumann boundary value problem for the $p$-Laplace equation

The Neumann boundary value problem for the $p$-Laplace equation with a low order term that does not satisfy the Bernstein–Nagumo condition was studied. The solvability of the problem in the class of radially symmetric solutions was investigated. A class of gradient nonlinearities was defined, for which the existence of a weak Sobolev radially symmetric solution that has a Hölder continuous derivative with exponent $\frac{1}{p-1}$ was proved.