Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations - Zuodong Yang (Boundary Value Problems, 2007)
We consider the problem Ã¢ÂˆÂ’div(|Ã¢ÂˆÂ‡u|pÃ¢ÂˆÂ’2Ã¢ÂˆÂ‡u)=a(x)(um+ÃŽÂ»un), xÃ¢ÂˆÂˆÃ¢Â„ÂN, NÃ¢Â‰Â¥3, where 0<m<pÃ¢ÂˆÂ’1<n,a(x)Ã¢Â‰Â¥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists ÃŽÂ»0>0 such that the above-mentioned equation admits at least one solution for all ÃŽÂ»Ã¢ÂˆÂˆ(0,ÃŽÂ»0). This extends the results of Laplace equation to the case of p-Laplace equation.