Nonradial large solutions for a class of nonlinear problems

Rhouma, Nedra Belhaj; Drissi, Amor; Wahid, Sayeb

doi:10.1080/17476933.2013.778838

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…By adjusting the above arguments, we are able to prove the below remark, which generalises the main result in [5].…”

supporting

confidence: 66%

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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“…By adjusting the above arguments, we are able to prove the below remark, which generalises the main result in [5].…”

supporting

confidence: 66%

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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show abstract

“…By adjusting the above arguments, we are able to prove the below remark, which generalises the main result in . Remark If we assume the stronger hypothesis

0true \overset{H}{true} : = \int_{0}^{\infty} true[η_{4} (a^{*} false(s false)) - η_{3} (a_{*} false(s false)) true] h^{- 1} true(s f true(F^{- 1} true(\int_{0}^{s} h^{- 1} ({scriptA}_{a^{*}} false(t false)) d t true) true) true) d s < \infty,

instead of

(F)

, we obtain the same results of Theorem with

\overset{H}{true}

in the place of

\bar{H}

, without assuming , where

a_{*} false(r false) = min false{a (x); false| x false| \leq r false}, a^{*} false(r false) = max false{a (x); false| x false| \leq r false}, r \geq 0 .

…”

Section: On Whole Rnsupporting

confidence: 56%

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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“…where v is the solution of (2.2) and the proof of the existence is similar to Theorem 3.1 in [2]. Suppose now that (1.1) has a large solution w in Ω.…”

Section: Nonradial Casementioning

confidence: 87%

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Song

Quan

et al. 2021

Asymptotic Analysis

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The aim of this paper is to consider the following fractional parabolic problem u t + ( − Δ ) p α u + ( − Δ ) q β u = f ( x , u ) ( x , t ) ∈ Ω × ( 0 , ∞ ) , u = 0 ( x , t ) ∈ ( R N ∖ Ω ) × ( 0 , ∞ ) , u ( x , 0 ) = u 0 ( x ) x ∈ Ω , where Ω ⊂ R N is a bounded domain with Lipschitz boundary, ( − Δ ) p α is the fractional p-Laplacian with 0 < α < 1 < p < ∞, ( − Δ ) q β is the fractional q-Laplacian with 0 < β < α < 1 < q < p < ∞, r > 1 and λ > 0. The global existence of nonnegative solutions is obtained by combining the Galerkin approximations with the potential well theory. Then, by virtue of a differential inequality technique, we give a decay estimate of solutions.

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Nonradial large solutions for a class of nonlinear problems

Cited by 4 publications

References 10 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

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

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