In this paper (which is a continuation of Part-I), we discuss the limit beh
aviour of solutions to boundary value problem with equivalued surface for p
-laplacian equations in the case of 1 < p <less than or equal to> 2 - 1/N w
hen the equivalued surface boundary shrinks to a point in certain way. Copy
right (C) 2001 John Wiley & Sons, Ltd.