The monotone minorant method and eigenvalue problem for multivalued operators in cones


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	The monotone minorant method and eigenvalue problem for multivalued operators in cones


	Fixed Point Theory, Volume 19, No. 1, 2018, 275-286, February 1st, 2018 DOI: 10.24193/fpt-ro.2018.1.22 Authors: Nguyen Bich Huy, Tran Thanh Binh and Vo Viet Tri Abstract: The main aim of this paper is to obtain a general theorem on existence of continuous branch of solutions of equations which depend on a parameter by using the monotone minorant method in conjunction with the theory of fixed point index. As an application, we apply this theorem to prove the existence of a positive eigen-pair of multivalued homogeneous increasing operators. The simplicity and uniqueness of the eigen-pair are also investigated in this paper. Key Words and Phrases: Cone, positive eigen-pair, fixed point index, monotone minorant, multivalued increasing operator. 2010 Mathematics Subject Classification: 47H04, 47H07, 47H10, 35P30. Published on-line: February 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents