Existence and Multiplicity of Positive Solutions for a System of Fourth-Order Boundary Value Problems
Keyword(s):
A Priori
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We study the existence and multiplicity of positive solutions for the system of fourth-order boundary value problems x(4)=ft,x,x′,-x′′,-x′′′,y,y′,-y′′,-y′′′, y(4)=gt,x,x′,-x′′,-x′′′,y,y′,-y′′,-y′′′, x(0)=x′(1)=x′′(0)=x′′′(1)=0, and y(0)=y′(1)=y′′(0)=y′′′(1)=0, where f,g∈C([0,1]×R+8,R+) (R+:=[0,∞)). We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and inequalities and R+2-monotone matrices.
2012 ◽
Vol 63
(9)
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pp. 1369-1381
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2012 ◽
Vol 252
(5)
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pp. 3403-3435
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