Existence Results for Singular Boundary Value Problems

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This monograph presents the existence and multiplicity of positive solutions to singular boundary value problems. The first part deals with the existence of positive periodic solutions for a singular system of first-order differential equations. In the second part, the authors are concerned with the discrete analogue of singular differential equations of second-order boundary value problems. By using the Krasnoselskii fixed point theorem on compression and expectation in cone, sufficient conditions for the existence of positive solutions are established for a singular system of first-order differential equations and singular second-order boundary value problems of difference equations. The results give an almost complete structure of the existence of positive solutions for the problems studied with an appropriately chosen parameter. By choosing appropriate cone, the singularity of the equations is essentially removed and the associated positive operator becomes well defined for certain ranges of functions. Clearly, this monograph contains an interesting and necessary material, which will be interesting for experts in the theory of boundary value problems of general form.