TY - JOUR
T1 - The existence of positive solutions for kirchhoff-type problems via the sub-supersolution method
AU - Yan, Baoqiang
AU - O’Regan, Donal
AU - Agarwal, Ravi P.
N1 - Publisher Copyright:
© 2018, Ovidius University. All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Existence
KW - Kirchhoff-type elliptic problems
KW - Rabinowitz-type global bifurcation theory
KW - Sub-supersolution method
KW - Uniqueness
UR - http://www.scopus.com/inward/record.url?scp=85045986903&partnerID=8YFLogxK
U2 - 10.2478/auom-2018-0001
DO - 10.2478/auom-2018-0001
M3 - Article
SN - 1224-1784
VL - 26
SP - 5
EP - 42
JO - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
JF - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
IS - 1
ER -