Existence and multiplicity results for some Lane–Emden elliptic systems: Subquadratic case

Barile, Sara; Salvatore, Addolorata

doi:10.1515/anona-2014-0049

Cited by 9 publications

(2 citation statements)

References 9 publications

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“…Systems of type (1.1) have also been studied in [10,16,17,19]. The singular semilinear case p 1 = p 2 = 2 in (1.2) has been studied even more frequently in [1,6,7,12,13,22]. For instance, if m = 2, p < 0 and q, r, s > 0, system (1.1) corresponds to Gierer-Meinhardt system [21] in morphogenesis.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Weak solutions for singular quasilinear elliptic systems

Singh

2016

Complex Variables and Elliptic Equations

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We investigate the quasilinear elliptic systemwhere Ω ⊂ R N (N ≥ 1) is a bounded and smooth domain, 1 < m < ∞, p, q, r, s > 0. Under certain conditions imposed on the exponents we obtain the existence and uniqueness of a weak solution (u, v) with u, v ∈ W 1,m 0(Ω) ∩ C(Ω). We also investigate the W 1,τ 0 (Ω) regularity of solution and determine the optimal range of τ ≥ m for such regularity.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Weak solutions for singular quasilinear elliptic systems

Singh

2016

Complex Variables and Elliptic Equations

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“…where f (x, u) = f (u) = u q−1 with q > 1 and 1 p + 1 q > 1. In this so called subquadratic case existence results have been established in [6], [9] and [17] in bounded domains. In the superquadratic but subcritical case, i.e.…”

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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Existence and Multiplicity for Quasi-Critical Fourth Order Quasilinear Problems with Generalized Vanishing Potentials

Barile

2016

J Elliptic Parabol Equ

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Existence and multiplicity results for some Lane–Emden elliptic systems: Subquadratic case

Cited by 9 publications

References 9 publications

Weak solutions for singular quasilinear elliptic systems

Weak solutions for singular quasilinear elliptic systems

Some New Results on Subquadratic Lane–Emden Elliptic Systems

Existence and Multiplicity for Quasi-Critical Fourth Order Quasilinear Problems with Generalized Vanishing Potentials

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