ON A SEMILINEAR ELLIPTIC EQUATION IN R(2) WHEN THE EXPONENT APPROACHES INFINITY

We consider a semilinear elliptic equation in R(2) with the nonlinear exponent approaching infinity. In contrast to the blow-up behavior of the corresponding problem in R'' with n greater than or equal to 3, th e L(x)(R(2)) norms of the solutions to the equation in R(2) remain bou nded from below and above. After a careful study on the decay rates of several quantities, we prove that the normalized solutions will appro ach the fundamental solution of -Delta + 1 in R(2). So as the exponent tends to infinity, the solutions to the problem look more and more li ke a peak. (C) 1995 Academic Press, lnc.