Weighted Elliptic Systems of Lane–Emden Type in Unbounded Domains

Barile, Sara; Salvatore, Addolorata

doi:10.1007/s00009-011-0149-1

Cited by 6 publications

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“…On the contrary, in the critical case 1 p + 1 q = 1 − 2 N , non-existence results have been stated in [23] and [27]. When ρ(x) = 0, problems like (1.1) have been studied in unbounded domains both in the superquadratic case in [3], [4] [5] and [11] and in the subquadratic case in the recent paper [7] by the same authors. Hereafter we study (1.1) under more general assumptions then those in [7] (see Example 1.4).…”

Section: Introductionmentioning

confidence: 99%

Some New Results on Subquadratic Lane–Emden Elliptic Systems

Barile

Salvatore

2017

Mediterr. J. Math.

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We deal with a nonlinear elliptic weighted system of Lane-Emden type in R N , N ≥ 3, by exploiting its equivalence with a fourth order quasilinear elliptic equation involving a suitable "sublinear" term. By overcoming the loss of compactness of the problem with some compact imbeddings in weighted L p-spaces, we establish existence and multiplicity results by means of a generalized Weierstrass Theorem and a variant of the Symmetric Mountain Pass Theorem stated by R. Kajikiya for subquadratic functionals. These results, which generalize previous ones stated by the same authors, apply in particular to a biharmonic equation under Navier conditions in R N .

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