带非奇扰动项的(2,p)-Laplace方程无穷多解的存在性

Existence of infinitely many solutions to(2, p)-Laplacian equations with non-odd perturbation terms

本文研究带非奇扰动项的(2,p)-Laplace方程{u=0,-△u-△pu=a(x)|u|^(q-2)u+f(x,u)x∈ЭΩ,x∈Ω,其中ΩСR^(N)是有界光滑区域,1<q<2<p<N,a∈C(Ω)可变号,f关于u不必是奇函数.利用变分方法,本文获得该方程无穷多解的存在性.

In this paper, the(2, p)-Laplacian equations with non-odd perturbation terms {u=0,-△u-△pu=a(x)|u|^(q-2)u+f(x,u)x∈ЭΩ,x∈Ω are considered, where ΩСR^(N) is a smooth bounded domain, 1 < q < 2 < p < N, a ∈ C(Ω) is allowed to change sign, and f may not be odd in u. Using the variational method, we obtain the existence of infinitely many solutions to the above equations.