一类广义Capillarity方程的单调性方法  

MONOTONICITY METHOD FOR A KIND OF GENERALIZED CAPILLARITY EQUATIONS

作　　者：魏利[1] 段丽凌[1] 

机构地区：[1]河北经贸大学数学与统计学学院,石家庄050061

出　　处：《系统科学与数学》2013年第8期937-948,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(11071053);河北省自然科学基金项目(A2010001482);河北省教育厅科学研究计划重点项目(ZH2012080);河北省教育厅科学研究计划青年项目(Q2012054);河北经贸大学科研重点项目(2013KYZ01)资助课题

摘　　要：利用变分不等式解的存在性的结论,证明了具有Dirichlet边值条件的广义Capillarity方程解的存在唯一性.借助于挖掘具有Dirichlet边值条件的广义Capillarity方程和具有Neumann边值条件的广义Capillarity方程之间的关系并利用极大单调算子值域的扰动结果,得到了具有Neumann边值条件的广义Capillarity方程解的存在性的一个充分条件.文中采用了一些新的证明技巧,推广和补充了笔者以往的一些研究工作.Based on some results on the existence of solutions for variational in- equalities, the existence and uniqueness of solution for a class of generalized capillarity equations with Dirichlet boundary value conditions are proved. By using the relation- ship between the capillarity equations with Neumann boudary value conditions and the capillarity equations with Dirichlet boundary value conditions and by employing a perturbation result on the ranges for maximal monotone operators, one sufficient condition of the existence of solution of the generalized capillarity equations with Neumann boundary value conditions is obtained. Some new methods are proposed in this paper, which extend and complement some existing ones.

关 键 词：极大单调算子 伪单调算子 广义Capillarity方程 Dirichlet边值条件 NEUMANN 边值条件 

分 类 号：O175[理学—数学]