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Existence and nonexistence of positive solutions for a class of third order BVP with integral boundary conditions in Banach spaces. (English) Zbl 1221.34053
Summary: We investigate the existence, nonexistence, and multiplicity of positive solutions for a class of nonlinear boundary-value problems of third order differential equations with integral boundary conditions in ordered Banach spaces by means of a fixed-point principle in cones and the fixed-point index theory for strict set contraction operators. In addition, an example is worked out to demonstrate the main results.

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ODE 34B18 Positive solutions of nonlinear boundary value problems for ODE 34G20 Nonlinear ODE in abstract spaces 47N20 Applications of operator theory to differential and integral equations
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##### References:
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