含有共振项的p-Laplace方程解的存在性

The Existence of Solution for p-Laplace Equation Involving Resonant Term

主要讨论一类非线性项在无穷远处渐近|u|^(p-2)u增长的p-Laplace方程的Dirichlet边值问题,利用环绕定理证明了当λ_1≤λ<(λ_1为算子(-△_p,W_1,p^0(Ω))第一特征值)时,方程存在非平凡解.

In this paper, a class of p-Laplace equations involving a term of asymptotically ｜u｜^p-2u at infinity are studied under the Dirichlet boundary condition. By applying the linking theorem, the existence of nontrivial solution is obtained when λ1 ≤ A 〈 λ2, where λ1 is the first eigenvalue of （-△p, W0^1,p B（Ω））.