Unilateral Global Bifurcation for Eigenvalue Problems with Homogeneous Operator
Unilateral Global Bifurcation for Eigenvalue Problems with Homogeneous Operator
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DOI：
10.1142/s0218127419500846
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Guowei Dai;Zhaosheng Feng
中科院分区：
文献类型：
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作者：
Guowei Dai;Zhaosheng Feng
我们关注非线性方程[公式：见正文]的解集的结构，其中[公式：见正文]和[公式：见正文]是连续算子。在[公式：见正文]和[公式：见正文]的某些假设下，给出了特征值问题的单侧整体分支。一些应用说明了非线性常微分方程和偏微分方程。特别地，讨论了Monge-Ampère方程单符号解的存在性和多重性.
We focus on the structure of the solution set for the nonlinear equation [Formula: see text] where [Formula: see text] and [Formula: see text] are continuous operators. Under certain hypotheses on [Formula: see text] and [Formula: see text], unilateral global bifurcations for eigenvalue problems are presented. Some applications are illustrated for nonlinear ordinary and partial differential equations. In particular, the existence and multiplicity of one-sign solutions for Monge–Ampère equation is discussed.