Global bifurcation phenomena for singular one-dimensional p-Laplacian
Global bifurcation phenomena for singular one-dimensional p-Laplacian
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DOI：
10.1016/j.jde.2006.03.021
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发表时间：
2006-10
影响因子：
2.4
通讯作者：
Yong-Hoon Lee;Inbo Sim
中科院分区：
文献类型：
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作者：
Yong-Hoon Lee;Inbo Sim
本文给出了φp(x)=|x|p−2x, p>1，λ为正参数，h为（0,1）上的非负可测函数，且该函数在t=0和/或t=1时可能是奇异的，且f∈C（R+,R+）与R+=[0，∞]的整体存在性结果。通过应用全局分岔定理和计算解的无界次连续线的形状，我们得到了许多不同类型的正解的全局存在性结果。我们还得到了当f是奇对称函数时（Pλ）变符号解的存在性结果。
In this paper, we present global existence results for the following problem where φp(x)=|x|p−2x, p>1,λ a positive parameter and h a nonnegative measurable function on (0,1) which may be singular at t=0 and/or t=1, and f∈C(R+,R+) with 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) when f is an odd symmetric function.