Uniqueness And Asymptotic Stability For The Radial Solutions Of Semilinear Elliptic Equations

Less is known of the uniqueness for the radial solutions u=ur of the problem &#916u + f(u+) = 0 in Rn(n>2), u (&#961) = 0, u\'(0) = 0 besides the cases where limr&#8594&#8734u(r)=0; and for the cases based only on the evolution of the functions f(t) and ddt f(t)t. This paper proves uniqueness for the problem Da+f(u+)=0 (r>0), u(&#961) = 0, u\'(0) = 0 based on the assumption that f &#8712C1([0,&#8734)) and that &#961 satisfies a boundedness condition. Furthermore, we prove asymptotic stability for Da+f(u+)=0 based only on the evolution of u\'(r) and u-&#966(r)f(u). Keywords: Semilinear elliptic equations, Radial solutions, uniqueness, compactness, asymptotic stabilityGlobal Journal of Mathematical Sciences Vol. 7 (1) 2008: pp. 53-5