AN LQ(RN)-THEORY OF SUBCRITICAL SEMILINEAR ELLIPTIC PROBLEMS

Existence and asymptotic decay estimates are obtained for solutions u ε{lunate} L 2N (N-2)(RN), N ≥ 3, of a class of semilinear elliptic problems including the subcritical Emden-Fowler type. The problems are not assumed to be radially symmetric. The method is based on the convergence in Cloc2(RN) of a sequence of "approximate solutions" uk ε{lunate} W01,2(RN) for which {uk} is bounded in LQ(RN) for all Q ≥ 2N (N - 2). In one case the solution is shown to have a removable singularity at ∞. © 1990.