Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4612710 | Journal of Differential Equations | 2006 | 28 Pages |
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
Yong-Hoon Lee, Inbo Sim,