On some multiple solutions for a p(x)-Laplacian equation with critical growth

• Published in: Journal of mathematical analysis and applications Vol. 436; no. 2; pp. 782 - 795
• Main Author: da Silva, João Pablo P.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.04.2016
• Subjects: [formula omitted]-Laplacian; Concentration compactness principle; Critical nonlinearity; Variational methods; p(x)-Laplacian; Concentration compactness principle; Variational methods; Critical nonlinearity
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2015.11.078

In this work we prove that, for each m∈N, if λ is small, there are m solutions for the equation −div(|∇u|p(x)−2∇u)=f(x,u)+λ|u|q(x)−2u, x∈Ω, in a bounded domain of RN, the nonlinearity is given by the critical growth in the context of variable exponents p⁎(x)=Np(x)/(N−p(x)). The main tools used are the variational method and concentration compactness principle.