Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems

Sun, Yijing; Wu, Shaoping; Ye, Long

doi:10.1006/jdeq.2000.3973

Cited by 139 publications

(20 citation statements)

References 14 publications

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“…In addition to the papers we already quoted we refer to [6], [7], [11], [13], [20], [21], [31], [34], [37], [38] and the references therein. An excellent starting point to these studies is the survey [19], where very extensive literature is available.…”

Section: Introductionmentioning

confidence: 99%

Existence and regularity results for fully nonlinear equations with singularities

2011

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Section: Introductionmentioning

confidence: 99%

Existence and regularity results for fully nonlinear equations with singularities

2011

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“…Historically, problem (P λ ) with M(x) = I has quite an extensive literature (see [3,4,5,6,7,8,9,10,11,12,13,14,15,16]) with their references therein. It seems that problem (P λ ), has attracted less attention.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A multiplicity result for a singular problem with subcritical nonlinearities

2017

J. Nonlinear Funct. Anal.

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“…When m is "small" enough, Coclite and Palmieri [10] prove the existence of a solution to problem (1.3) for 0 < λ < Λ, for some Λ < ∞. Assuming −1 < α < 0, Yijing et al [36] apply variational arguments based on Nehari's method [28] to show the existence of at least two solutions for q ∈ (1, 2…”

Section: Definition 11mentioning

confidence: 99%

Uniqueness and multiplicity results for N-Laplace equation with critical and singular nonlinearity in a ball

Giacomoni

Prashanth²,

Sreenadh

2009

Asymptotic Analysis

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Let B 1 be the unit open ball with center at the origin in R N , N 2. We consider the following quasilinear problem depending on a real parameter λ > 0:where f (t) is a nonlinearity that grows like e t N/N −1 as t → ∞ and behaves like t α , for some α ∈ (−∞, 0), as t → 0 + . More precisely, we require f to satisfy assumptions (A1) and (A2) listed in Section 1. For such a general nonlinearity we show that if λ > 0 is small enough, (P λ ) admits at least one weak solution (in the sense of distributions). We further study the question of uniqueness and multiplicity of solutions to (P λ ) when Ω = B 1 under additional structural conditions on f (see assumptions (A3)-(A8) in Section 2). Using shooting methods and asymptotic analysis of ODEs, under the additional assumptions (A3)-(A5), we prove uniqueness of solution to (P λ ) for all λ > 0 small whereas under (A6), (A7) or (A8), we show multiplicity of solutions to (P λ ) for all λ > 0 in a maximal interval. These results clearly show that the borderline between uniqueness and multiplicity is given by the growth condition lim inf t→∞ h(t)te εt 1/(N −1) = ∞ ∀ε > 0.

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Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems

Abstract: This paper deals with a class of singular semilinear elliptic Dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results.

Cited by 139 publications

References 14 publications

Existence and regularity results for fully nonlinear equations with singularities

Existence and regularity results for fully nonlinear equations with singularities

A multiplicity result for a singular problem with subcritical nonlinearities

Uniqueness and multiplicity results for N-Laplace equation with critical and singular nonlinearity in a ball

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