Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616929 | Journal of Mathematical Analysis and Applications | 2013 | 23 Pages |
Abstract
In this work, we study the following boundary value problem (P){−div(a(|∇u|)∇u)=f(x,u),in Ω,u=0,on ∂Ω, with nonhomogeneous principal part. By assuming the nonlinearity f(x,t)f(x,t) corresponds to subcritical growth, we prove a regularity result for weak solutions. Using the regularity result we show that C1C1-local minimizers are also local minimizers in the Orlicz–Sobolev space. So, similar to the approach for the pp-Laplacian equation, the sub–supersolution method for this problem is developed. Applying these results and critical point theory, we prove the existence of multiple solutions of problem (P) in the Orlicz–Sobolev space. The result for the sign-changing solution is new for the pp-Laplacian equation.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zhong Tan, Fei Fang,