Positive solutions with specific asymptotic behavior for a polyharmonic problem on Rn

Tyt. z nagłówka.Bibliogr. s. 18-19.his paper is concerned with positive solutions of the semilinear polyharmonic equation [formula] on Rn, where m and n are positive integers with n > 2m, α ∈ e (—1,1). The coefncient a is assumed to satisfy[formula], where Λ ∈ (2m,∞)and [formula]is ositive wuth [formula], one also assumes that[formula]. We prove the existence of a positive solution u such that [formula], with [formula]and a function L, given explicitly in terms of L and satisfying the same condition as infinity. (Given positive functions ∫ and g on Rn, ∫≈ g means that [formula]for some constant c > 1.)Dostępny również w formie drukowanej.KEYWORDS: asymptotic behavior, Dirichlet problem, Schauder fixed point theorem, positive bounded solutions