Global bifurcation phenomena for singular one-dimensional p-Laplacian

In this paper, we present global existence results for the following problemequation(Pλ){φp(u′(t))′+λh(t)f(u(t))=0,a.e. in(0,1),u(0)=u(1)=0, where φp(x)=|x|p−2xφp(x)=|x|p−2x, p>1,λp>1,λ a positive parameter and h   a nonnegative measurable function on (0,1)(0,1) which may be singular at t=0t=0 and/or t=1t=1, and f∈C(R+,R+)f∈C(R+,R+) with R+=[0,∞)R+=[0,∞). By applying the global bifurcation theorem and figuring the shape of unbounded subcontinua of solutions, we obtain many different types of global existence results of positive solutions. We also obtain existence results of sign-changing solutions for (Pλ)(Pλ) when f is an odd symmetric function.