The purpose of this paper is to find a criterion of partial integrability for general nonlinear systems. Here partial integrability means the existence of a certain numbers of first integrals less than the number required for the complete integration [10]. We also give an algebraic criterion of partial integrability for general semi-quasihomogeneous systems. (2000). 58F07. Mathematics Subject Classification

In this paper we study a singularly perturbed nonlinear partial differential system which arises in the mathematical theory of superheating field of superconductivity. We prove that the maximum points of the magnitude of solutions are located near the minimum point of curvature of domain boundary. This verifies rigorously a result of Chapman obtained by formal analysis regarding the location of the vortex nucleation. We also show that the solutions exhibit boundary layers. # 2002 Elsevier Science (USA)

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