Existence of Solutions

of Singular Initial and Boundary Value Problems

V.Lakshmikantham, J.V.Devi

Florida Institute of Technology

Melbourne, FL 32901, USA

Recently there has been much activity concerning the existence of solutions of singular initial and boundary value problems. By utilizing the standard method of lower and upper solutions to generate a sequence of solutions of nonsingular problems suitably, one can extend the classical method to prove the existence results for singular problems. This approach simplifies the proofs in the literature and brings out clearly the ideas involved. In this paper, we discuss some recent results relative to initial and boundary value problems in ordinary and partial differential equations. Here it is considered: Singular Initial Value Problems, Singular Boundary Value Problems, Singular Elliptic Boundary Value Problems.