Multiplicity of positive solutions for p-Laplace equation with superlinear-type nonlinearity

摘要

In this work, we consider the problem{-Delta (p)u = u(p* + uq) }((P)())(R) } in B-R(0), { u > 0 } { u =0 on dB(R)(0)where p > 2, p* =Np/(N - p) and BR(O) is the open ball of radius R centered about the origin in RN, N greater than or equal to 3. Under the condition that p - 1 < q < P-2 /(N - p)-1 , we show that there exists R-* > 0 such that (P-R) admits atleast two solutions for all Ris an element of (R-*, infinity) and no solution if R < R-*. This extends the results of (Nonlinear Anal. TMA 10(8) (1986) 755) to the case of p-Laplace equation. (C) 2003 Elsevier Ltd. All rights reserved.