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On the oscillation of solutions of partial differential equations in three variables. (English) Zbl 1267.35017
J. Sov. Math. 64, No. 5, 1159-1163 (1993); translation from Mat. Metody Fiz.-Mekh. Polya, No. 32, 45-48 (1990).
Summary: We obtain conditions for oscillation and nonoscillation of solutions of the equation \(Lu+pu=0\) in Euclidean, spherical, and hyperbolic spaces with three variables, and also direct and converse theorems on mean values over spheres.
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
44A12 Radon transform
Full Text: DOI
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