Quasilinearization and multiple solutions of the Emden‐Fowler type equation

Abstract

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.

Emdeno‐Faulerio tipo lygties kvazelinerizavimas ir daugialypiai sprendiniai

Darbe nagrinėjamas taip vadinamas Emdeno‐Faulerio kvazitiesinės diferencialinės lygties homogeninio kraštinio uždavinio sprendinių egzistavimas ir daugialypumas. Parodyta, kad šio uždavinio sprendinio daugialypumas priklauso nuo tam tikru būdu gautos kvazilinearizuotos lygties tiesinės dalies savybių.

First Published Online: 14 Oct 2010

Keyword : quasi‐linear equation, i‐nonresonant linear part, i‐type solution, quasi‐linearization