论文标题
弱上半连续扰动的准$ m $ $ $ accretive操作员学位
Degree for weakly upper semicontinuous perturbations of quasi-$m$-accretive operators
论文作者
论文摘要
在本文中，我们提供了巧合学位的构造，是一个同质副本不变的，以检测f（x）$，$ x \ in U $中的方程解决方案或表格的夹杂物的存在，其中$ a \ colon d（a）\ multiMap E $是Banach Space $ e $，$ f \ COLON K \ MULTIMAP E $中的$ M $ accretive运算符，这是一个弱上的半连续的设置值，被限制在封闭的$ k \ subset e $的开放子集$ u $上。将提出两种不同的方法。该理论用于表明某些具有不连续性的非线性二阶偏微分方程的非平凡阳性解的存在。
In the paper we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an $m$-accretive operator in a Banach space $ E$, $F\colon K\multimap E$ is a weakly upper semicontinuous set-valued map constrained to an open subset $U$ of a closed set $K\subset E$. Two different approaches will be presented. The theory is applied to show the existence of nontrivial positive solutions of some nonlinear second order partial differential equations with discontinuities.
