On the perturbed eigenvalue problem
The author considers the perturbed eigenvalue problem \(L(x) v(x)= \lambda(x) v(x)\) near \(0= x\in \mathbb{R}\) with \(L(x)\) a Fredholm operator of index zero. Using the implicit function theorem and the bordering lemma, he derives a necessary and sufficient smoothness condition for the characteristic pairs \((\lambda(x), v(x))\) with eigenvalue \(\lambda(x)\) emanating from a semi-simple eigenvalue \(\lambda(0)\) of \(L(0)\).
scientific article; zbMATH DE number 755529