Existence and uniqueness of positive solution for nonhomogeneous sublinear elliptic equations

AbstractIn this paper, we study the existence and the uniqueness of positive solution for the sublinear elliptic equation, −Δu+u=|u|psgn(u)+f in RN, N⩾3, 0<p<1, f∈L2(RN), f>0 a.e. in RN. We show by applying a minimizing method on the Nehari manifold that this problem has a unique positive solution in H1(RN)∩Lp+1(RN). We study its continuity in the perturbation parameter f at 0