Minimax principles for convex eigenvalue problems

Theodore Laetsch

doi:10.1016/0022-247X(84)90174-4

Minimax principles for convex eigenvalue problems

Theodore Laetsch

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Positive solutions of the nonlinear eigenvalue problem Au = σu for a forced, convex, isotone, compact operator on a partially ordered locally convex topological vector space E are considered. Denote by σ^* the infimum of the set of σ for which the equation has a solution u in the positive cone K of E. σ^* is characterized as the saddle value of a functional J_A determined by A and defined on the Cartesian product of K and its dual K^*.

Original language	English (US)
Pages (from-to)	328-347
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	102
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(84)90174-4
State	Published - Sep 1984

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-247X(84)90174-4

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title = "Minimax principles for convex eigenvalue problems",

abstract = "Positive solutions of the nonlinear eigenvalue problem Au = σu for a forced, convex, isotone, compact operator on a partially ordered locally convex topological vector space E are considered. Denote by σ* the infimum of the set of σ for which the equation has a solution u in the positive cone K of E. σ* is characterized as the saddle value of a functional JA determined by A and defined on the Cartesian product of K and its dual K*.",

author = "Theodore Laetsch",

year = "1984",

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doi = "10.1016/0022-247X(84)90174-4",

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journal = "Journal of Mathematical Analysis and Applications",

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N2 - Positive solutions of the nonlinear eigenvalue problem Au = σu for a forced, convex, isotone, compact operator on a partially ordered locally convex topological vector space E are considered. Denote by σ* the infimum of the set of σ for which the equation has a solution u in the positive cone K of E. σ* is characterized as the saddle value of a functional JA determined by A and defined on the Cartesian product of K and its dual K*.

AB - Positive solutions of the nonlinear eigenvalue problem Au = σu for a forced, convex, isotone, compact operator on a partially ordered locally convex topological vector space E are considered. Denote by σ* the infimum of the set of σ for which the equation has a solution u in the positive cone K of E. σ* is characterized as the saddle value of a functional JA determined by A and defined on the Cartesian product of K and its dual K*.

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U2 - 10.1016/0022-247X(84)90174-4

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M3 - Article

AN - SCOPUS:0021500395

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SP - 328

EP - 347

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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Minimax principles for convex eigenvalue problems

Abstract

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