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Positive solutions and eigenvalues of conjugate boundary value problems

Published online by Cambridge University Press:  20 January 2009

Ravi P. Agarwal ,
Martin Bohner  and
Patricia J. Y. Wong
Ravi P. Agarwal
Affiliation:
National University of Singapore, Department of Mathematics, 10 Kent Ridge Crescent, Singapore119260 E-mail address: matravip@leonis.nus.sg martin@saturn.sdsu.edu
Martin Bohner
Affiliation:
National University of Singapore, Department of Mathematics, 10 Kent Ridge Crescent, Singapore119260 E-mail address: matravip@leonis.nus.sg martin@saturn.sdsu.edu
Patricia J. Y. Wong
Affiliation:
Nanyang Technological University, Division of Mathematics, 469 Bukit Timah Road, Singapore, 259756 E-mail address: wongjyp@nievax.nie.ac.sg
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We consider the following boundary value problem

where λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 349 - 374
Copyright
Copyright © Edinburgh Mathematical Society 1999

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