Lu Feng-Yun, Deng Gui-Qian
Xingyi Normal University for Nationalities, Xingyi, Guizhou 562400, China ; Human Resources and Social Security Bureau, Buyi and Miao Autonomous Prefecture in Southwest Guizhou, Guizhou 562400, China.
Xingyi Normal University for Nationalities, Xingyi, Guizhou 562400, China.
ScientificWorldJournal. 2014 Jan 14;2014:194310. doi: 10.1155/2014/194310. eCollection 2014.
We study the following p-Laplacian equation with nonlinear boundary conditions: -Δ(p)u + μ(x)|u|(p-2)u = f(x,u) + g(x,u),x ∈ Ω, | ∇u|(p-2)∂u/∂n = η|u|(p-2)u and x ∈ ∂Ω, where Ω is a bounded domain in ℝ(N) with smooth boundary ∂Ω. We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and f, g do not need to satisfy the (P.S) or (P.S*) condition.
我们研究如下具有非线性边界条件的(p -)拉普拉斯方程：(-\Delta_p u+\mu(x)|u|^{p - 2}u = f(x,u)+g(x,u))，(x\in\Omega)，(|\nabla u|^{p - 2}\frac{\partial u}{\partial n}=\eta|u|^{p - 2}u)且(x\in\partial\Omega)，其中(\Omega)是(\mathbb{R}^N)中具有光滑边界(\partial\Omega)的有界区域。我们利用邹（2001）提出的变分喷泉定理证明该方程有无限多个弱解，并且(f)、(g)不需要满足((P.S))或((P.S^*))条件。
