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Existence of positive solutions for higher-order generalized p-Laplacian BVPs

โœ Scribed by Wei-Cheng Lian; Fu-Hsiang Wong

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
353 KB
Volume
13
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

In this paper, we provide suitable conditions on the function f (t, ul,..., un-1) such that the higher-order generalized p-Laplacian boundary value problem

has at least one positive solution. Moreover, we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions. (~) 2000 Elsevier Science Ltd, All rights reserved. Keywords--Positive solutions, Existence, Concavity, Fixed-point theorem in cones and higherorder BVPs.

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We shall provide conditions on non-positive function f(t, uj .... ,u,-1) so that the boundary value problem (BVP) for t E (0, 1) and n ~>2, ## ~u~-2~(0) -flu~"-~(O) = O, ?u("-2)(1) + 6u ~n l)(1) = 0, has at least one positive solution. Then, we shall apply this result to establish several existe