Mean-value theorems and the nonoscillatory nature of solutions of partial differential equations in the spaces En and Pn

Analogs of the mean-value theorem are obtained for the Poisson equation with the Laplace-Beltrami operator in Euclidean and spherical spaces.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1477–1483, November, 1992.