Asymptotic Behavior of Radial Solutions for a Class of Semilinear Elliptic Equations

Abstract

Equation (1) has its origin from, e.g., the prescribed curvature problems in Riemannian geometry, and astrophysics (i.e., the Lane Emden Fowler equation and the Matukuma equation as special cases). The asymptotic behavior of the positive solutions to (1) has recently received much attention, see e.g., [L1, LN, Na]. However, it is well-known that the above equation (1) does not always have positive solutions or positive radial solutions. In other words, under suitable conditions, radial solutions to (1) must oscillate about the zero at infinite times (see e.g., [DCC, NY, N]). Thus it becomes very interesting to know as precisely as possible the asympototic behaviors of the oscillating periods, the amplitudes of the oscillatory solutions. In this paper, we restrict our attention to the study of radial solutions to (1). More precisely, we shall discuss the asymptotic behavior of oscillatory article no. DE963208