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Existence of positive solutions for [formula omitted]order [formula omitted]-Laplacian BVP

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
53
Issue
9
Identifiers
DOI: 10.1016/j.camwa.2006.05.023
Keywords
  • Existence Of Positive Solutions
  • [Formula Omitted]Order Bvp
  • [Formula Omitted]-Laplacian

Abstract

Abstract Under some suitable assumptions, we show that the n + 2 order non-linear boundary value problems ( BVP 1 ) { ( E 1 ) [ ϕ p ( u ( n ) ( t ) ) ] ″ = f ( t , u ( t ) , u ( 1 ) ( t ) , … , u ( n + 1 ) ( t ) ) ( BC 1 ) { u ( i ) ( 0 ) = 0 , i = 0 , 1 , 2 , … , n − 3 , u ( n − 1 ) ( 1 ) = 0 u ( n − 2 ) ( 0 ) = λ u ( n − 1 ) ( η ) u ( n + 1 ) ( 0 ) = α 1 u ( n + 1 ) ( ξ ) u ( n ) ( 1 ) = β 1 u ( n ) ( ξ ) and ( BVP 2 ) { ( E 2 ) [ ϕ p ( u ( n ) ( t ) ) ] ″ = f ( t , u ( t ) , u ( 1 ) ( t ) , … , u ( n + 1 ) ( t ) ) ( BC 2 ) { u ( i ) ( 0 ) = 0 , i = 0 , 1 , 2 , … , n − 3 , u ( n − 1 ) ( 0 ) = 0 u ( n − 2 ) ( 1 ) = − λ u ( n − 1 ) ( η ) u ( n + 1 ) ( 0 ) = α 1 u ( n + 1 ) ( ξ ) u ( n ) ( 1 ) = β 1 u ( n ) ( ξ ) have at least two positive solutions in C n [ 0 , 1 ] .

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