TY - JOUR
T1 - Minimax principles for convex eigenvalue problems
AU - Laetsch, Theodore
PY - 1984/9
Y1 - 1984/9
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*.
UR - http://www.scopus.com/inward/record.url?scp=0021500395&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0021500395&partnerID=8YFLogxK
U2 - 10.1016/0022-247X(84)90174-4
DO - 10.1016/0022-247X(84)90174-4
M3 - Article
AN - SCOPUS:0021500395
SN - 0022-247X
VL - 102
SP - 328
EP - 347
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -