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We establish the
existence of positive solutions for singular boundary value problems of coupled
The proof relies on Schauder’s fixed point theorem. Some recent results
in the literature are generalized and improved.
By mixed monotone method, we establish the existence and uniqueness of
positive solutions for fourth-order nonlinear singular Sturm-Liouville
problems. The theorems obtained are very general and complement previously
By fixed point theorem of a mixed
monotone operator, we study boundary value problems to nonlinear singular
fourth-order differential equations, and provide sufficient conditions for the
existence and uniqueness of positive solution. The nonlinear term in the differential
equation may be singular.