TY - JOUR
T1 - Positive solutions of even order periodic boundary value problems
AU - Kong, Qingkai
AU - Wang, Min
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2011
Y1 - 2011
N2 - We study a class of periodic boundary value problems associated with even order differential equations. By applying the Krasnosel'skii fixed point theorem and the fixed point index theory, we establish a series of criteria for the problem to have one, two, an arbitrary number, and even an infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also derived. These criteria are given by explicit conditions which are easy to verify. Several examples are provided to show the applications. Our results extend, improve and supplement many results in the literature, even for the second order case.
AB - We study a class of periodic boundary value problems associated with even order differential equations. By applying the Krasnosel'skii fixed point theorem and the fixed point index theory, we establish a series of criteria for the problem to have one, two, an arbitrary number, and even an infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also derived. These criteria are given by explicit conditions which are easy to verify. Several examples are provided to show the applications. Our results extend, improve and supplement many results in the literature, even for the second order case.
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U2 - 10.1216/RMJ-2011-41-6-1907
DO - 10.1216/RMJ-2011-41-6-1907
M3 - Article
AN - SCOPUS:84863292741
VL - 41
SP - 1907
EP - 1931
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
SN - 0035-7596
IS - 6
ER -