Large and entire large solutions for a class of nonlinear problems

Rhouma, Nedra Belhaj; Drissi, Amor

doi:10.1016/j.amc.2014.01.008

Cited by 5 publications

(5 citation statements)

References 8 publications

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“…in the place of (1.5). In the line of the previous results, recently, Rhouma and Drissi [6] considered…”

Section: Introductionsupporting

confidence: 60%

See 1 more Smart Citation

Necessary and sufficient conditions for existence of Blow-up solutions for elliptic problems in Orlicz-Sobolev spaces

Santos¹,

Zhou²,

Santos³

2016

Preprint

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This paper is principally devoted to revisit the remarkable works of Keller and Osserman and generalize some previous results related to the those for the class of quasilinear elliptic problemwhere either Ω ⊂ R N with N ≥ 1 is a smooth bounded domain or Ω = R N . The function φ includes special cases appearing in mathematical models in nonlinear elasticity, plasticity, generalized Newtonian fluids, and in quantum physics. The proofs are based on comparison principle, variational methods and topological arguments on the Orlicz-Sobolev spaces.

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“…in the place of (1.5). In the line of the previous results, recently, Rhouma and Drissi [6] considered…”

Section: Introductionsupporting

confidence: 60%

“…Recently, Zhang in [30] considered the p(x)−Laplacian operator in the problem (1.1). About Ω = R N , the problem (1.1) was considered in [6] and references therein with φ(t) = p|t| p−2 , t > 0 and 2 ≤ p ≤ N .…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for existence of Blow-up solutions for elliptic problems in Orlicz-Sobolev spaces

Santos¹,

Zhou²,

Santos³

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…Keeping us in this context, Mabroux and Hansen in improved the above results by considering

0true \int_{0}^{\infty} r a_{o s c} (r) {false(1 + \underset{̲}{A} (r) false)}^{γ / false(1 - γ false)} d r < \infty

in the place of . In the line of the previous results, recently, Rhouma and Drissi considered

ϕ false(t false) = {| t |}^{p - 2}, t \in R

, with

2 \leq p \leq N

, f a differentiable function that includes

u^{γ}

with

0 < γ \leq 1

, and they established necessary and sufficient conditions for existence of solutions for around the term a .…”

Section: Introductionmentioning

confidence: 89%

“…Recently, Zhang in considered the

p (x)

‐Laplacian operator in the problem . About

Ω = {boldR}^{N}

, the problem was considered in and references therein with

ϕ false(t false) = {p | t |}^{p - 2}

t > 0

and

2 \leq p \leq N

.…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces

Santos

Zhou

Santos

2017

Mathematische Nachrichten

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This paper is principally devoted to revisit the remarkable works of Keller and Osserman and generalize some previous results related to the those for the class of quasilinear elliptic problem { div ϕfalse(false|∇ufalse|false)∇u=afalse(xfalse)ffalse(ufalse)inΩ,u≥0inΩ,u=∞on∂Ω,where either Ω⊂boldRN with N≥1 is a smooth bounded domain or Ω=boldRN. The function ϕ includes special cases appearing in mathematical models in nonlinear elasticity, plasticity, generalized Newtonian fluids, and in quantum physics. The proofs are based on comparison principle, variational methods and topological arguments on the Orlicz–Sobolev spaces.

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“…More exactly, he assumed ∞ 0 ra osc (r)exp(A(r))dr < ∞, where A(r) = r 0 sa(s)ds, r ≥ 0 and proved that (1.3), with suitable f that includes u γ for 0 < γ ≤ 1, admits a solution if, and only if, (1.5) holds with a in the place of a. Keeping us in this context, we also quote Rhouma and Drissi [3] for 2 ≤ p ≤ N , and references therein.…”

Section: Introductionmentioning

confidence: 98%

Infinite many Blow-up solutions for a Schrödinger quasilinear elliptic problem with a non-square diffusion term

Santos¹,

Zhou²

2016

Preprint

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Large and entire large solutions for a class of nonlinear problems

Cited by 5 publications

References 8 publications

Necessary and sufficient conditions for existence of Blow-up solutions for elliptic problems in Orlicz-Sobolev spaces

Necessary and sufficient conditions for existence of Blow-up solutions for elliptic problems in Orlicz-Sobolev spaces

Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces

Infinite many Blow-up solutions for a Schrödinger quasilinear elliptic problem with a non-square diffusion term

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