On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems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

On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems

Authors:

Affiliation:

(1) Department of Mathematics, Faculty of Engineering, Tokushima University, Tokushima 770-8506, Japan;(2) Department of Mathematics, Naruto University of Education, Takashima, Naruto 772-8502, Japan

Abstract:

We study a quasilinear elliptic problem

$$ left{begin{array}{ll} -,{rm div}(phi(|nabla u|)nabla u) = lambda f(x,u) &quadtext{in ${rm Omega}$} u = 0 &quadtext{on $partial{rm Omega}$}end{array}right.$$

with nonhomogeneous principal part φ. Under the hypothesis f(x,t)= o(φ(t)t) at t= 0 and ∞, the existence of multiple positive solutions is proved by using the variational arguments in the Orlicz–Sobolev spaces. Mathematics Subject Classification (2000) 35J20; 35J25; 35J70; 47J10; 47J30

Keywords:

Quasilinear elliptic problem Multiple positive solutions Orlicz– Sobolev spaces

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