A-priori bounds and asymptotics on the eigenvalues in bifurcation problems for perturbed self-adjoint operators
A-priori bounds and asymptotics on the eigenvalues in bifurcation problems for perturbed self-adjoint operators
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扰动自伴算子分岔问题特征值的先验界和渐近性
DOI：
10.1016/j.jmaa.2008.12.061
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发表时间：
2009
影响因子：
1.3
通讯作者：
R. Chiappinelli
中科院分区：
文献类型：
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作者：
R. Chiappinelli
我们证明了上界和下界的特征值和讨论其渐近行为（作为范数的特征向量趋于零）在分歧问题的平凡的解决方案，考虑扰动的线性自伴算子在Hilbert空间。证明是基于Lyapounov-Schmidt约化。所得结果应用于RN有界域上的一类半线性椭圆算子，特别是Sturm-Liouville算子.
We prove upper and lower bounds on the eigenvalues and discuss their asymptotic behaviour (as the norm of the eigenvector tends to zero) in bifurcation problems from the line of trivial solutions, considering perturbations of linear self-adjoint operators in a Hilbert space. The proofs are based on the Lyapounov–Schmidt reduction. The results are applied to a class of semilinear elliptic operators in bounded domains of RNand in particular to Sturm–Liouville operators.
非线性 Sturm-Liouville 问题的精确谱渐近
DOI：
--
发表时间：
2002
期刊：
Journal of Differential Equations 180
影响因子：
--
作者：
Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata;Tetsutaro Shibata
通讯作者：
Tetsutaro Shibata