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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.
MSC:
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
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References:
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