SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS

Let ? denote a smooth, bounded domain in R^N(N≥2). Suppose that g is a nondecreasing C¹ positive function and assume that b(x) is continuous and nonnegative in?, and that it may be singular on ??. In this paper, we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem ?_pu = b(x)g(u) for x∈?, u(x)→+∞ as dist(x, ??)→0.The estimates of such solutions are also investigated. Moreover, when b has strong sin...