具有临界增长边界条件的p-Laplace方程解的存在性

Existence of Weak Solutions for the p-Laplace Equation with Critical Growth in Boundary Conditions

考虑了具有临界增长边界条件的拟线性椭圆方程,得到的主要结果如下:若f关于u是超线性次临界增长,则当p<r<p*时,应用"山路引理"证明了方程至少存在一个非平凡的弱解;当1<r<p时,应用"对偶喷泉定理"和"集中紧性原理"证明了方程无穷多弱解的存在性。

To consider the critical growth in boundary conditions for the quasilinear problem, the main results are obtained that iffhas superlinear but subcritical growth with respect to u , then as p 〈 r 〈p ^＊, there exists at least one nontrivial weak solution by using ＂mountain pass theorem＂ ; as 1 〈 r 〈 p , there exists infinitely many weak solutions by using ＂dual fountain theorem＂ and ＂concentration-compactness principle＂.