A NEW THEME IN NONLINEAR ANALYSIS: CONTINUATION AND BIFURCATION OF THE UNIT EIGENVECTORS OF A PERTURBED LINEAR OPERATOR
A NEW THEME IN NONLINEAR ANALYSIS: CONTINUATION AND BIFURCATION OF THE UNIT EIGENVECTORS OF A PERTURBED LINEAR OPERATOR
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非线性分析的一个新主题：摄动线性算子的单位特征向量的延拓和分叉
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Pera
中科院分区：
文献类型：
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作者：
R. Chiappinelli;Massimo Furi;M. Pera
我们回顾了关于形如(∗)au+ǫB(U)=δu的非线性特征值问题的一些最新结果，其中A是作用在实Banach空间X上的指数为零(具有非平凡核的)的线性→算子，B：X FredholmX是(可能的)非线性摄动项。我们在X的单位球面上求(∗)的解u，重点是在适当的条件下，存在点u0∈S∩Ker A(从而满足(∗)ǫ=δ=0)，它可以作为(∗)的解继续下去，或者--更一般地--是这类解的分歧点。
We review some recent results concerning nonlinear eigenvalue problems of the form (∗) Au + ǫB(u) = δu, where A is a linear Fredholm operator of index zero (with nontrivial kernel Ker A) acting in a real Banach space X, and B : X → X is a (possibly) nonlinear perturbation term. We seek solutions u of (∗) in the unit sphere S of X, and the emphasis is put on the existence - under appropriate conditions on B - of points u0 ∈ S ∩ Ker A (thus satisfying (∗) for ǫ = δ = 0) which either can be continued as solutions of (∗) for ǫ 6 0 or - more generally - are bifurcation points for solutions of that kind.