Solving an abstract nonlinear eigenvalue problem by the inverse iteration method

Abstract

Let $\left(X,{\Vert \cdot \Vert }_X\right)$ and $\left(Y,{\Vert \cdot \Vert }_Y\right)$ be Banach spaces over $\mathbb{R},$ with $X$ uniformly convex and compactly embedded into $Y.$ The inverse iteration method is applied to solve the abstract eigenvalue problem $A(w)=\lambda {\Vert w\Vert }_Y^{p-q}B(w),$ where the maps $A:X\to X^{\star }$ and $B:Y\to Y^{\star }$ are homogeneous of degrees $p-1$ and $q-1,$ respectively.

This paper generalizes, for an abstract setting, another previously posted in ArXiv (see arXiv:1510.03941v2), which has not been submitted to or published in any other source

Cited by in corpus (2)

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