Existence of a positive solution for a p-Laplacian semipositone problem

We consider the boundary value problem ￠ ’ ”pu= f(u) in satisfying u=0 on ￠ , where u=0 on ￠ , >0 is a parameter, is a bounded domain in ￠ n with C2 boundary ￠ , and ”pu:=div(| ￠ u|p ￠ ’2 ￠ u) for p>1. Here, f:[0,r] ￠ ’ ￠ is a C1 nondecreasing function for some r>0 satisfying f(0)<0 (semipositone). We establish a range of for which the above problem has a positive solution when f satisfies certain additional conditions. We employ the method of subsuper solutions to obtain the result.