The existence of positive solutions for kirchhoff-type problems via the sub-supersolution method
Agarwal, Ravi P.
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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
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.