Abstract
We study the eigenvalue problems for a class of positive nonlinear operators defined on a cone in a Banach space. Using projective metric techniques and Schauder’s fixed-point theorem, we establish existence, uniqueness, monotonicity and continuity results for the eigensolutions. Moreover, the method leads to a result on the existence of a unique fixed point of the operator. Applications to nonlinear boundary-value problems, to differential delay equations and to matrix equations are considered.
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Huang, MJ., Huang, CY. & Tsai, TM. Eigenvalue problems and fixed point theorems for a class of positive nonlinear operators. Math. Z. 257, 581–595 (2007). https://doi.org/10.1007/s00209-007-0136-1
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DOI: https://doi.org/10.1007/s00209-007-0136-1