具有非线性边界条件的p-拉普拉斯方程的无穷多个弱解。
Infinitely many weak solutions of the p-Laplacian equation with nonlinear boundary conditions.
作者信息
Lu Feng-Yun, Deng Gui-Qian
机构信息
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.
出版信息
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。
Zotero 插件