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Zbl 1221.34053
Zhao, Junfang; Wang, Peiguang; Ge, Weigao
Existence and nonexistence of positive solutions for a class of third order BVP with integral boundary conditions in Banach spaces. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 402-413 (2011). ISSN 1007-5704

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 2000:: *34B10 Multipoint boundary value problems
34B18 Positive solutions of nonlinear boundary value problems
34G20 Nonlinear ODE in abstract spaces
47N20 Appl. of operator theory to differential and integral equations

Keywords: third order; positive solutions; fixed-point index theory; boundary-value problem; integral boundary condition; measure of noncompactness

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