Continuous spectrum for a class of nonhomogeneous differential operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Continuous spectrum for a class of nonhomogeneous differential operators

Authors:	Mihai Mihăilescu Vicenţiu Rădulescu

Affiliation:	(1) Department of Mathematics, University of Craiova, 200585 Craiova, Romania;(2) Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania

Abstract:	We study the boundary value problem $-{rm div}((\|nabla u\|^{p_1(x)-2}+\|nabla u\|^{p_2(x)-2})nabla u)=lambda\|u\|^{q(x)-2}u$ in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in $mathbb{R}^N$ with smooth boundary, λ is a positive real number, and the continuous functions p ₁, p ₂, and q satisfy 1 < p ₂(x) < q(x) < p ₁(x) < N and $max_{yinoverlineOmega}q(y) < frac{N p_2(x)}{N-p_2(x)}$ for any . The main result of this paper establishes the existence of two positive constants λ₀ and λ₁ with λ₀ ≤ λ₁ such that any is an eigenvalue, while any is not an eigenvalue of the above problem.

Keywords:	35D05 35J60 35J70 58E05 68T40 76A02
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