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Multiple solutions for 2mth-order Sturm-Liouville boundary value problems

✍ Scribed by Chuan Jen Chyan; J. Henderson


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
352 KB
Volume
40
Category
Article
ISSN
0898-1221

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✦ Synopsis


Growth conditions are imposed on f such that the following boundary value problem:

(-1)my (2m) = f(t,y), o~i+ly(2i)(0) -f~i+ly(2/+l)(0) --7i+ly(2i)(1) + 5i+1y(2i+1)(1) = O, 0 < i < m-1, has an arbitrary number of positive solutions. (~) 2000 Elsevier Science Ltd. All rights reserved.


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Positive solutions of 2mth-order boundar
✍ Chuan Jen Chyan; J. Henderson πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 471 KB

We study the existence of positive solutions of the differential equation (-l)my(2m) (t) = f(t,y(t),y"(t), . . ,y(2(m-'))(t)) with the boundary condition Y(~~)(O) = 0 = I, 0 5 i 5 m -1, and Y(~~)(O) = 0 = y( 2i+1)(l), 0 5 i 5 m -1. We show the existence of at least one positive solution if f is eith

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In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions for the third-order Sturm-Liouville boundary value problem with p-Laplacian where Ο† p (s) = |s| p-2 s, p > 1. As an application, an example is given to demonstrate the