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Positive solutions for second order boundary value problems with derivative terms
Author(s) -
Li Yongxiang
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500040
Subject(s) - sublinear function , mathematics , fixed point index , boundary value problem , nonlinear system , order (exchange) , mathematical analysis , derivative (finance) , second derivative , value (mathematics) , statistics , physics , finance , quantum mechanics , financial economics , economics
This paper weals with the existence of positive solutions of the fully second‐order boundary value problem− u ′ ′( t ) = f ( t , u ( t ) ,u ′ ( t ) ) , t ∈ [ 0 , 1 ] ,u ( 0 ) = u ( 1 ) = 0 ,where f : [ 0 , 1 ] × R + × R → R +is continuous. Under the conditions that the nonlinearity f ( t , x , y ) may be superlinear or sublinear growth on x and y , the existence results of positive solutions are obtained. For the superlinear case, a Nagumo‐type condition is presented to restrict the growth of f on y . The superlinear and sublinear growth of the nonlinearity f are described by inequality conditions instead of the usual upper and lower limits conditions. Our discussion is based on the fixed point index theory in cones.