ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR SUBLINEAR AND SINGULAR NONLINEAR DIRICHLET PROBLEMS

In this article, we are concerned with the asymptotic behavior of the classical solution to the semilinear boundary-value problem Delta u + a(x)u(sigma) = 0 in R-n, u > 0, lim(vertical bar x vertical bar -> infinity) u(x) = 0, where sigma < 1. The special feature is to consider the function a in C-loc(alpha)(R-n), 0 < alpha < 1, such that there exists c > 0 satisfying 1/c L(vertical bar x vertical bar + 1)/(1 + vertical bar x vertical bar)(lambda) <= a(x) <= c L(vertical bar x vertical bar + 1)/(1 + vertical bar x vertical bar)(lambda), where L(t) := exp (integral(t)(1) z(s)/s ds), with z is an element of C([1, infinity)) such that lim(t -> infinity) z(t) = 0. The comparable asymptotic rate of a(x) determines the asymptotic behavior of the solution.