Eigenvalue problems and fixed point theorems for a class of positive nonlinear operators |
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| Authors: | Min-Jei Huang Chao-Ya Huang Tzong-Mo Tsai |
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| Institution: | (1) Department of Mathematics, National Tsing Hua University, Hsinchu, 30043, Taiwan;(2) Department of Electrical Engineering, Mingchi University of Technology, Taishan, Taipei, 24301, Taiwan |
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| 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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| Keywords: | Eigenvalue problem Fixed point Cone Projective metric Concave operator Compact operator |
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