摘要
This paper is concerned with the bounded value problems1/p（t）（p（t）u’）’+f（u）=0, t】0, u’（0）=0, lim t→+∞ u（t）=0,where f（0）=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R<sup>n</sup>. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p（t）=f<sup>n-1</sup>and f（u）=u<sup>P</sup>-u, where n】1, p】1 are some given constants.
This paper is concerned with the bounded value problems1/p(t)(p(t)u')'+f(u)=0, t>0, u'(0)=0, lim t→+∞ u(t)=0,where f(0)=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R^n. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p(t)=f^(n-1)and f(u)=u^P-u, where n>1, p>1 are some given constants.
基金
This work was partially supported by Institute of Mathematics,Academia Sinica.
