一类椭圆型变分不等式的非平凡广义解的存在性(英文)

The Existence of Nontrivial Solutions to a Class of Elliptic Variational Inequalities

本文研究了下列障碍问题的非平凡解的存在性u∈K∶∫Ωu.(u-u)dx+∫Ωa(x)u.(v-u)dx∫Ωp(x,u)(v-u)dx,v∈K.其中K={v∈H01(Ω)∶vψa.e.onΩ}.利用关于不等式推广的山路引理,在a(x)和障碍p(x,ξ)满足适当的假设下,我们证明了上述不等式存在非平凡解.

In this paper,we study the existence of nontrivial solutions of the obstacle problem：u∈K：∫Ω↓△u·↓△（u-u）dx＋∫Ωa（x）u·（v-u）dx≥∫ΩP（x,u）（v-u）,arbitary v∈K.whereK={v∈H0^1（Ω）：v≤ψa.e.onΩ}.By using a generalized mountain pass theorem for inequalities,we prove,subject to some conditions on the obstacle and above inequalities.