Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global persistence of the unit eigenvectors of perturbed eigenvalue
  problems in Hilbert spaces   We consider the nonlinear eigenvalue problem $Lx + \varepsilon N(x) = \lambda
Cx$, $\|x\|=1$, where $\varepsilon,\lambda$ are real parameters, $L, C\colon G
\to H$ are bounded linear operators between separable real Hilbert spaces, and
$N\colon S \to H$ is a continuous map defined on the unit sphere of $G$. We
prove a global persistence result regarding the set $\Sigma$ of the solutions
$(x,\varepsilon,\lambda) \in S \times \mathbb R\times \mathbb R$ of this
problem. Namely, if the operators $N$ and $C$ are compact, under suitable
assumptions on a solution $p_*=(x_*,0,\lambda_*)$ of the unperturbed problem,
we prove that the connected component of $\Sigma$ containing $p_*$ is either
unbounded or meets a triple $p^*=(x^*,0,\lambda^*)$ with $p^* \not= p_*$. When
$C$ is the identity and $G=H$ is finite dimensional, the assumptions on
$(x_*,0,\lambda_*)$ mean that $x_*$ is an eigenvector of $L$ whose
corresponding eigenvalue $\lambda_*$ is simple. Therefore, we extend a previous
result obtained by the authors in the finite dimensional setting. Our work is
inspired by a paper of R. Chiappinelli concerning the local persistence
property of the unit eigenvectors of perturbed self-adjoint operators in a real
Hilbert space.

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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin