The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method-Reference-Cited by-同舟云学术

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

Published:2018-03-01 Issue:1 Volume:26 Page:5-41
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Yan Baoqiang¹,O’Regan Donal²,Agarwal Ravi P.³

Affiliation:

1. School of Mathematical Sciences, Shandong Normal University, Jinan , 250014, P. R. China

2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway , Ireland

3. Department of Mathematics, Texas A and M University-Kingsville, Texas 78363, USA

Abstract

Abstract In this paper we discuss the existence of a solution between wellordered 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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2018-0001

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