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On the cardinality of solutions of multilinear differential equations and applications. (English) Zbl 0663.34008
The author considers differential equations of the form \(Mu=(L_ 1u)(L_ 2u)...(L_ mu)=0,\) where \(L_ i=\sum^{n(i)}_{j=0}c_{ij}D^ j,\) n(1)\(\geq...\geq n(m)\), \(i=1,...,m\), in the space \(C^{n(1)}[a,b]\), \(c_{ij}\in C^{n(1)}[a,b]\). He obtains necessary and sufficient conditions in order that the given equation have branching solutions of a given form, and studies their cardinality. He considers the initial problem in a neighborhood of a branching point. He applies the results obtained to specific equations, constructs solutions, and gives their quantitative estimate in various cases.
34A30 Linear ordinary differential equations and systems
34A99 General theory for ordinary differential equations
Full Text: DOI EuDML