The Existence of Nontrivial Weak Solutions of a Class of p-Laplacian Equationt without Compactness
PU Zhi-lin · Journal of Sichuan Normal University · 2006
This paper deals with the p-Laplacian equations such as-div(|x|~α|u|~(p-2)u)+b(x)|u|~(p-1)=f(x,u).By selecting the appropriate space and approximating the bounded domain to the boundless domain,we overcome the difficulty of lack of compactness and obtain the the existence of nontrivial weak solutions in R~N with Caffarelli-Kohn-Nirenberg inequality and the mountain-pass-theorem without the(PS) condition.