Existence and multiplicity of solutions of the problem x” = ‐q(t) |x|p sign x (i), x(0) = x(1) = 0 (ii) are investigated by reducing equation (i) to a quasi‐linear one so that both equations are equivalent in some domain O. If a solution of corresponding quasi‐linear problem is located in the domain of equivalence O, then this solution solves the original problem also. If this process of quasilinearization is possible for multiple essentially different linear parts, then multiple solutions to the problem (i), (ii) exist. Darbe nagrinejamas taip vadinamas Emdeno‐Faulerio kvazitiesines diferencialines lygties homogeninio kraštinio uždavinio sprendiniu egzistavimas ir daugialypumas. Parodyta, kad šio uždavinio sprendinio daugialypumas priklauso nuo tam tikru būdu gautos kvazilinearizuotos lygties tiesines dalies savybiu.

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Abstract. We study the structure of attractors in the two-dimensional dynamical− x2 that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

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