关于一类带次临界指标的拟线性薛定谔方程的正解

The positive solutions for subcritical quasilinear Schrdinger equations

主要考虑一类拟线性薛定谔方程的正解,由于该方程所对应泛函不能定义在常用空间H1(RN)上,而且H1(RN)→嵌入Lq(RN)(2<Q<2*)是非紧的,利用变量替换能够使得泛函在H1(RN)上有定义,并且Strauss证明了H1(RN)的径向空间H1(RN),而且H1(RN)→嵌入Lq(RN)(2<Q<2*)是紧的,从而利用山路引理证明所研究方程存在正解.

We considered the generalized quasilinear Schr6dinger equations, and so the functional for the equations didn＇t he defined in the space H1 （R^N）. To overcome this difficuhy, we made a variable replacement, the new function was well defined in H1 （RN）, in addition, the embedding H1（R^N）→Lq（R^N） （2〈Q〈2＊） was not compact, fortunately, Strauss proved that the embedding HI（R^N）→Lq （RN） （2〈Q〈2＊） was compact, where H1 （RN） was the radial space of U1 （RN）, therefore, we obtained the positive solutions for the studied equations by mountain pass lemma and maximum principle.