Existence and multiplicity of positive solutions for one-dimensional $ p $-Laplacian problem with sign-changing weight

Abstract

In this paper, we show the positive solutions set for one-dimensional $ p $-Laplacian problem with sign-changing weight contains a reversed $ S $-shaped continuum. By figuring the shape of unbounded continuum of positive solutions, we identify the interval of bifurcation parameter in which the $ p $-Laplacian problem has one or two or three positive solutions according to the asymptotic behavior of nonlinear term at 0 and $ \infty $. The proof of the main result is based upon bifurcation technique.