EXISTENCE OF RADIAL SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN EQUATIONS WITH CRITICAL GROWTH

Author(s)

Alves, Claudianor O. ^[1]

Affiliation

^[1] Univ Fed Campina Grande, Unidade Acad Matemat & Estat, BR-58109970 Campina Grande, PB - Brazil

• Document type: Journal article
• Source: DIFFERENTIAL AND INTEGRAL EQUATIONS; v. 23, n. 1-2, p. 113-123, JAN-FEB 2010.
• Web of Science Citations: 12

Abstract

Using variational methods we establish the existence of solutions for the following class of p(x)-Laplacian equations -div(vertical bar del u vertical bar(p(x)-2)del u)+vertical bar u vertical bar(p(x)-2)u=lambda vertical bar u vertical bar(q(x)-2)u+vertical bar u vertical bar(p){*}((x)-2)u, R(N), (P) where lambda is an element of (0, infinity) is a parameter and p(x), q(x) R(N) -> R are radial continuous functions satisfying 1 < p(x) < N and p(x) << q(x) << p{*}x = p(x)N/N-p(x). (AU)