Article ID Journal Published Year Pages File Type
4612710 Journal of Differential Equations 2006 28 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
, ,