Abstract
This paper is devoted to the existence of radially-symmetric solutions of the boundary value problems as well as of the Cauchy problem, for the equation u t = eΔu+F(t, x, u, *u). We suppose that F(t, x, u, p) does not satisfy Bernstein's condition on no more than quadratic growth with respect to p when ‖p‖ ‖ → +∞. Conditions which guarantee the global solvability of the problems are formulated.
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