BIFURCATION AND MULTIPLICITY RESULTS FOR A NONHOMOGENEOUS SEMILINEAR ELLIPTIC PROBLEM

In this article we consider the problem -Delta u(x) + u(x) = lambda(a(x)u(p) + h(x)) in R-N, u is an element of H-1(R-N), u > 0 in R-N, where lambda is a positive parameter. We assume there exist mu > 2 and C > 0 such that a(x) - 1 >= -Cc(-mu|x|) for all x is an element of R-N. We prove that there exists a positive lambda* such that there are at least two positive solutions for lambda is an element of(0, lambda*) and a unique positive solution for lambda = lambda*. Also we show that (lambda*, u(lambda*)) is a bifurcation point in C-2,C-alpha(R-N) boolean AND H-2(R-N).