Nonlinear eigenvalue problems in Sobolev spaces with variable exponent
نویسندگان
چکیده
منابع مشابه
Nonlinear eigenvalue problems in Sobolev spaces with variable exponent
Abstract. We study the boundary value problem −div((|∇u|1 + |∇u|2)∇u) = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R . We focus on the cases when f±(x, u) = ±(−λ|u| u+ |u|u), where m(x) := max{p1(x), p2(x)} < q(x) < N ·m(x) N−m(x) for any x ∈ Ω. In the first case we show the existence of infinitely many weak solutions for any λ > 0. In the second case we prove that if λ is...
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ژورنال
عنوان ژورنال: Journal of Function Spaces and Applications
سال: 2006
ISSN: 0972-6802
DOI: 10.1155/2006/515496