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Existence and asymptotic behavior of positive solutions of a semilinear elliptic system in a bounded domain

Chaieb M., Dhifli A., Zermani S.

Opuscula Mathematica

2016

Vol. 36, no. 3

315--336

Let Ω be a bounded domain in [formula] with a smooth boundary [formula]. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system [formula] Here r, s ∈ R, α, β < 1 such that γ := (1 - α) (1 - β ) - rs > 0 and the functions [formula] are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.

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

Dhifli A.

Opuscula Mathematica

2015

Vol. 35, no. 1

5--19

This 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 positive with [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.)