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The existence of positive solutions for kirchhoff-type problems via the sub-supersolution method

Yan, Baoqiang
; 
O’Regan, Donal
; 
Agarwal, Ravi P.
Identifiers
http://hdl.handle.net/10379/14479
https://doi.org/10.13025/27467
Repository DOI
10.2478/auom-2018-0001
Publication Date
2018-03-01
Keywords
kirchhoff-type elliptic problems, rabinowitz-type global bifurcation theory, sub-supersolution method, existence, uniqueness, boundary-value problem, asymptotic-behavior, equation, singularity, diffusion, r-3
Type
Article
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Citation
Yan, Baoqiang; O’Regan, Donal; Agarwal, Ravi P. (2018). The existence of positive solutions for kirchhoff-type problems via the sub-supersolution method. Analele Universitatii "Ovidius" Constanta - Seria Matematica 26 (1), 5-41
Abstract
In this paper we discuss the existence of a solution between well ordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.
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Publisher
Walter de Gruyter GmbH
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)