On the partial quasi-analyticity of generalized solutions of weakly nonlinear differential equations with weighted derivatives

In this paper the author deals with sufficient conditions under which the set of generalized solutions of weakly nonlinear equations forms a partial quasi-analytic class. Applications are given to several classes of nonlinear wave-type equations, including the Kolmogorov-Petrovskiĭ-Piskunov-type equation, the Schrödinger-type equation, etc. The arguments used in the proof are based on the author's earlier results concerning linear equations [Mat. Sb. {bf 191} (2000), no.~3, 113--142; [msn] MR1773257 (2001i:35036) [/msn]].