Abstract
Let \(\left( X,\left\| \cdot \right\| _{X}\right) \) and \(\left( Y,\left\| \cdot \right\| _{Y}\right) \) 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 \(A(w)=\lambda \left\| w\right\| _{Y}^{p-q}B(w),\) where the maps \(A:X\rightarrow X^{\star }\) and \(B:Y\rightarrow Y^{\star }\) are homogeneous of degrees \(p-1\) and \(q-1,\) respectively.
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The author was supported by CNPq/Brazil (483970/2013-1 and 306590/2014-0) and Fapemig/Brazil (CEX APQ 03372/16).
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Ercole, G. Solving an Abstract Nonlinear Eigenvalue Problem by the Inverse Iteration Method. Bull Braz Math Soc, New Series 49, 577–591 (2018). https://doi.org/10.1007/s00574-018-0070-3
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DOI: https://doi.org/10.1007/s00574-018-0070-3