非线性退缩椭圆型方程Dirichlet问题多重解的存在性

The Existence of Multiple Solutions of Nonlinear Degenerate Elliptic Equations

本文利用临界点理论,研究一类非线性退缩椭圆型方程Dirichlet问题多解性。在嵌入非紧的条件下,证明泛函在给定集上满足(PS)条件。

Let Ω be a bounded domain with smooth boundary Ω and let Lu≡ where and Consider the following Dirichlet problem: where λ≥0, p = q0-1,q0=2n/(n-2+n/s), s >n/2. We obtain the following result: Theorem 1. Suppose that f(x,t) satisfies conditions (f1)-(f4). Then there exists a sequence of numbers {μk} μ1>μ2>…>μk>μk+1>…>0, such that for every λ∈[μk, μk-1] there are at least k distinct pairs of solutions of Dirichlet problem (P).