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Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives. (26th June 2013)
Record Type:
Journal Article
Title:
Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives. (26th June 2013)
Main Title:
Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives
Abstract : By using a fixed point theorem in a cone and the nonlocal third-order BVP's Green function, the existence of at least one positive solution for the third-order boundary-value problem with the integral boundary conditions x ′′′ ( t ) + f ( t, x ( t ), x ′ ( t ) ) = 0, t ∈ J, x ( 0 ) = 0, x ′′ ( 0 ) = 0, and x ( 1 ) = ∫ 0 1 g ( t ) x ( t ) d t is considered, where f is a nonnegative continuous function, J = [ 0, 1 ], and g ∈ L [ 0, 1 ] . The emphasis here is that f depends on the first-order derivatives.