临界增长的 P-Laplace 方程正解的存在性

THE EXISTENCE OF POSITIVE SOLUTION OF A P LAPLACE EQUATION INVOLVING CRITICAL INCREASING

利用｜Ｄｕ｜ｐ－２Ｄｉｕ在Ｓｈｏｂｏｌｅｖ空间中的弱连续和没有（ＰＳ）条件的山路引理及集中紧原理，讨论了ＲＮ中有界域Ω上一类拟线临界增长的椭圆型方程解的存在性，并在一定的假设条件下，证明了临界增长的Ｐ－Ｌａｐａｌａｃｅ方程存在正解。

By applying the weak continuity of |Du| P-2 D iu in Sebolev space and mountain pass lemma without(PS) condition and the concentration compactness principles,this paper have discussed the existence of solution for the quasilinear elliptil equation on bounded domain on  R N .It has been proved that the above P Laplace equation involling critical increasing has at least a positive solution in some suitable assumptions.