Topological degree theories and nonlinear operator equations in Banach spaces
Let \(X\) be a real Banach space, \(G_1\), \(G_2\) open and bounded such that \(0\in G_2\subset\bar{G}_2\subset G_1\). Let \(T:D(T)\to X\) be accretive such that \(0\in D(T)\) and \(T(0)=0\). Let \(C:D(C)\to X\) be compact or continuous and bounded with the resolvents of \(T\) compact. The authors use various degree theories to find zeros of \(T+C\) in \(D(T+C)\cap(G_1\setminus G_2)\). As a matter of fact, the article contains much more results: the range space may be \(X^*\) instead of \(X\) and \(C\) may belong to more complicated classes of operators. There is a short application to partial differential equations.
scientific article; zbMATH DE number 5323989
scientific article