Positive solutions of some elliptic differential equations with oscillating nonlinearity

Fahd Jarad; Octavian G. Mustafa; Donal O'Regan

doi:10.1080/17476933.2010.504836

Positive solutions of some elliptic differential equations with oscillating nonlinearity

Fahd Jarad
, Octavian G. Mustafa
, Donal O'Regan

Mathematics

Cankaya University
University of Craiova

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

We discuss the occurrence of positive solutions which decay to 0 as {pipe}x{pipe} →+∞ to the differential equation Δu + f(x, u) + g({pipe}x{pipe})x · ∇u = 0, {pipe}x{pipe}>R>0, x ∈ ℝ ⁿ, where n ≥ 3, g is nonnegative valued and f has alternating sign, by means of the comparison method. Our results complement several recent contributions from Ehrnström and Mustafa [M. Ehrnström, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), pp. 1147-1154].

Original language	English
Pages (from-to)	599-609
Number of pages	11
Journal	Complex Variables and Elliptic Equations
Volume	57
Issue number	6
DOIs	https://doi.org/10.1080/17476933.2010.504836
Publication status	Published - Jun 2012

Keywords

comparison method
elliptic partial differential equation
positive solution
sign changing nonlinearity

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10.1080/17476933.2010.504836

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title = "Positive solutions of some elliptic differential equations with oscillating nonlinearity",

abstract = "We discuss the occurrence of positive solutions which decay to 0 as \{pipe\}x\{pipe\} →+∞ to the differential equation Δu + f(x, u) + g(\{pipe\}x\{pipe\})x · ∇u = 0, \{pipe\}x\{pipe\}>R>0, x ∈ ℝ n, where n ≥ 3, g is nonnegative valued and f has alternating sign, by means of the comparison method. Our results complement several recent contributions from Ehrnstr{\"o}m and Mustafa [M. Ehrnstr{\"o}m, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), pp. 1147-1154].",

keywords = "comparison method, elliptic partial differential equation, positive solution, sign changing nonlinearity",

author = "Fahd Jarad and Mustafa, \{Octavian G.\} and Donal O'Regan",

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language = "English",

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T1 - Positive solutions of some elliptic differential equations with oscillating nonlinearity

AU - Jarad, Fahd

AU - Mustafa, Octavian G.

AU - O'Regan, Donal

PY - 2012/6

Y1 - 2012/6

N2 - We discuss the occurrence of positive solutions which decay to 0 as {pipe}x{pipe} →+∞ to the differential equation Δu + f(x, u) + g({pipe}x{pipe})x · ∇u = 0, {pipe}x{pipe}>R>0, x ∈ ℝ n, where n ≥ 3, g is nonnegative valued and f has alternating sign, by means of the comparison method. Our results complement several recent contributions from Ehrnström and Mustafa [M. Ehrnström, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), pp. 1147-1154].

AB - We discuss the occurrence of positive solutions which decay to 0 as {pipe}x{pipe} →+∞ to the differential equation Δu + f(x, u) + g({pipe}x{pipe})x · ∇u = 0, {pipe}x{pipe}>R>0, x ∈ ℝ n, where n ≥ 3, g is nonnegative valued and f has alternating sign, by means of the comparison method. Our results complement several recent contributions from Ehrnström and Mustafa [M. Ehrnström, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), pp. 1147-1154].

KW - comparison method

KW - elliptic partial differential equation

KW - positive solution

KW - sign changing nonlinearity

UR - https://www.scopus.com/pages/publications/84859914659

U2 - 10.1080/17476933.2010.504836

DO - 10.1080/17476933.2010.504836

M3 - Article

SN - 1747-6933

VL - 57

SP - 599

EP - 609

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 6

ER -

Positive solutions of some elliptic differential equations with oscillating nonlinearity

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